All basic nacci constants up to degree 13

Here are 7,500 of them, sorted by their digits:

All nacci constants starting with 1.0...

All nacci constants starting with 1.1...

All nacci constants starting with 1.2...

All nacci constants starting with 1.3...

All nacci constants starting with 1.4...

All nacci constants starting with 1.5...

All nacci constants starting with 1.6...

All nacci constants starting with 1.7...

All nacci constants starting with 1.8...

All nacci constants starting with 1.9...


There are infinitely many regular, predictable polynomials for each particular nacci number as one of their solutions.

Note: Based on E. Galois and Abel, polynomials of a degree higher than 4 cannot be solved (with few exceptions). However, by solving them with matrices, recursive formulas and rationals that converge to the real solution, it is possible to give each number with a 10,000 digit accuracy (see each particular link). Here are some examples:

1.05705057522...
`x^13 - x = 1` (12)
`x^25 - x^12 - x = 1` (13-11)
`x^37 - x^24 - x^12 - x = 1` (13-[12]-11)
...

1.05961102145...
`x^13 - x^2 = 1` (11)
`x^24 - x^11 - x^2 = 1` (13-9)
`x^35 - x^22 - x^11 - x^2 = 1` (13-[11]-9)
...

1.06216916786...
`x^12 - x = 1` (11)
`x^23 - x^11 - x = 1` (12-10)
`x^34 - x^22 - x^11 - x = 1` (12-[11]-10)
...

1.06250870523...
`x^13 - x^3 = 1` (10)
`x^23 - x^10 - x^3 = 1` (13-7)
`x^33 - x^20 - x^10 - x^3 = 1` (13-[10]-7)
...

1.06582624405...
`x^13 - x^4 = 1` (9)
`x^22 - x^9 - x^4 = 1` (13-5)
`x^31 - x^18 - x^9 - x^4 = 1` (13-[9]-5)
...

1.06829718892...
`x^11 - x = 1` (10)
`x^21 - x^10 - x = 1` (11-9)
`x^31 - x^20 - x^10 - x = 1` (11-[10]-9)
...

1.06967836633...
`x^13 - x^5 = 1` (8)
`x^21 - x^8 - x^5 = 1` (13-3)
`x^29 - x^16 - x^8 - x^5 = 1` (13-[8]-3)
...

1.07203255224...
`x^11 - x^2 = 1` (9)
`x^20 - x^9 - x^2 = 1` (11-7)
`x^29 - x^18 - x^9 - x^2 = 1` (11-[9]-7)
...

1.07423032257...
`x^13 - x^6 = 1` (7)
`x^20 - x^7 - x^6 = 1` (13-1)
`x^27 - x^14 - x^7 - x^6 = 1` (13-[7]-1)
...

1.07576606609...
`x^10 - x = 1` (9)
`x^19 - x^9 - x = 1` (10-8)
`x^28 - x^18 - x^9 - x = 1` (10-[9]-8)
...

1.07637950368...
`x^11 - x^3 = 1` (8)
`x^19 - x^8 - x^3 = 1` (11-5)
`x^27 - x^16 - x^8 - x^3 = 1` (11-[8]-5)
...

1.07766033457...
`x^12 - x^5 = 1` (7)
`x^19 - x^7 - x^5 = 1` (12-2)
`x^26 - x^14 - x^7 - x^5 = 1` (12-[7]-2)
...

1.07973135192...
`x^13 - x^7 = 1` (6)
`x^19 - x^7 - x^6 = 1` (12-1)
`x^25 - x^12 - x^7 - x^6 = 1` (13-5-1)
`x^31 - x^18 - x^12 - x^7 - x^6 = 1` (13-[6]-5-1)
...

1.08152908669...
`x^11 - x^4 = 1` (7)
`x^18 - x^7 - x^4 = 1` (11-3)
`x^25 - x^14 - x^7 - x^4 = 1` (11-[7]-3)
...

1.08507024549...
`x^9 - x = 1` (8)
`x^17 - x^8 - x = 1` (9-7)
`x^25 - x^16 - x^8 - x = 1` (9-[8]-7)
...

1.08593791264...
`x^10 - x^3 = 1` (7)
`x^17 - x^7 - x^3 = 1` (10-4)
`x^24 - x^14 - x^7 - x^3 = 1` (10-[7]-4)
...

1.08658059655...
`x^13 - x^8 = 1` (5)
`x^18 - x^8 - x^5 = 1` (10-3)
`x^23 - x^10 - x^8 - x^5 = 1` (13-2-3)
`x^28 - x^15 - x^10 - x^8 - x^5 = 1` (13-[5]-2-3)
...

1.08777020051...
`x^11 - x^5 = 1` (6)
`x^17 - x^6 - x^5 = 1` (11-1)
`x^23 - x^12 - x^6 - x^5 = 1` (11-[6]-1)
...

1.09079559658...
`x^12 - x^7 = 1` (5)
`x^17 - x^7 - x^5 = 1` (10-2)
`x^22 - x^10 - x^7 - x^5 = 1` (12-3-2)
`x^27 - x^15 - x^10 - x^7 - x^5 = 1` (12-[5]-3-2)
...

1.09102447048...
`x^9 - x^2 = 1` (7)
`x^16 - x^7 - x^2 = 1` (9-5)
`x^23 - x^14 - x^7 - x^2 = 1` (9-[7]-5)
...

1.09547157458...
`x^13 - x^9 = 1` (4)
`x^17 - x^9 - x^4 = 1` (8-5)
`x^21 - x^9 - x^8 - x^4 = 1` (12-1-4)
`x^25 - x^12 - x^9 - x^8 - x^4 = 1` (13-3-1-4)
`x^29 - x^16 - x^12 - x^9 - x^8 - x^4 = 1` (13-[4]-3-1-4)
...

1.0955668827...
`x^11 - x^6 = 1` (5)
`x^16 - x^6 - x^5 = 1` (10-1)
`x^21 - x^10 - x^6 - x^5 = 1` (11-4-1)
`x^26 - x^15 - x^10 - x^6 - x^5 = 1` (11-[5]-4-1)
...

1.09612898958...
`x^13 - x^2 - x = 1` (11-1)
`x^25 - x^14 - x^12 - x^2 - x = 1` (11-[2-10]-1)
...

1.0969815578...
`x^8 - x = 1` (7)
`x^15 - x^7 - x = 1` (8-6)
`x^22 - x^14 - x^7 - x = 1` (8-[7]-6)
...

1.09940979574...
`x^13 - x^3 - x = 1` (10-2)
`x^25 - x^15 - x^12 - x^3 - x = 1` (10-[3-9]-2)
...

1.10536732295...
`x^12 - x^2 - x = 1` (10-1)
`x^23 - x^13 - x^11 - x^2 - x = 1` (10-[2-9]-1)
...

1.10572820369...
`x^11 - x^7 = 1` (4)
`x^15 - x^7 - x^4 = 1` (8-3)
`x^19 - x^8 - x^7 - x^4 = 1` (11-1-3)
`x^23 - x^12 - x^8 - x^7 - x^4 = 1` (11-[4]-1-3)
...

1.10735199066...
`x^9 - x^4 = 1` (5)
`x^14 - x^5 - x^4 = 1` (9-1)
`x^19 - x^10 - x^5 - x^4 = 1` (9-[5]-1)
...

1.10776045679...
`x^13 - x^10 = 1` (3)
`x^16 - x^10 - x^3 = 1` (6-7)
`x^19 - x^10 - x^6 - x^3 = 1` (9-4-3)
`x^22 - x^10 - x^9 - x^6 - x^3 = 1` (12-1-3-3)
`x^25 - x^12 - x^10 - x^9 - x^6 - x^3 = 1` (13-2-1-3-3)
`x^28 - x^15 - x^12 - x^10 - x^9 - x^6 - x^3 = 1` (12-[3]-2-1-3-3)
...

1.10936927345...
`x^12 - x^3 - x = 1` (9-2)
`x^23 - x^14 - x^11 - x^3 - x = 1` (9-[3-8]-2)
...

1.11277568428...
`x^7 - x = 1` (6)
`x^13 - x^6 - x = 1` (7-5)
`x^19 - x^12 - x^6 - x = 1` (7-[6]-5)
...

1.11479780585...
`x^8 - x^3 = 1` (5)
`x^13 - x^5 - x^3 = 1` (8-2)
`x^18 - x^10 - x^5 - x^3 = 1` (8-[5]-2)
...

1.11657515837...
`x^11 - x^2 - x = 1` (9-1)
`x^21 - x^12 - x^10 - x^2 - x = 1` (9-[2-8]-1)
...

1.11925266658...
`x^9 - x^5 = 1` (4)
`x^13 - x^5 - x^4 = 1` (8-1)
`x^17 - x^8 - x^5 - x^4 = 1` (9-3-1)
`x^21 - x^12 - x^8 - x^5 - x^4 = 1` (9-[4]-3-1)
...

1.11984287664...
`x^11 - x^8 = 1` (3)
`x^14 - x^8 - x^3 = 1` (6-5)
`x^17 - x^8 - x^6 - x^3 = 1` (9-2-3)
`x^20 - x^9 - x^8 - x^6 - x^3 = 1` (11-1-2-3)
`x^23 - x^12 - x^9 - x^8 - x^6 - x^3 = 1` (11-[3]-1-2-3)
...

1.12156494465...
`x^11 - x^3 - x = 1` (8-2)
`x^21 - x^13 - x^10 - x^3 - x = 1` (8-[3-7]-2)
...

1.123732821...
`x^7 - x^2 = 1` (5)
`x^12 - x^5 - x^2 = 1` (7-3)
`x^17 - x^10 - x^5 - x^2 = 1` (7-[5]-3)
...

1.12665248353...
`x^13 - x^11 = 1` (2)
`x^15 - x^11 - x^2 = 1` (4-9)
`x^17 - x^11 - x^4 - x^2 = 1` (6-7-2)
`x^19 - x^11 - x^6 - x^4 - x^2 = 1` (8-5-2-2)
`x^21 - x^11- x^8 - x^6 - x^4 - x^2 = 1` (10-3-2-2-2)
`x^23 - x^11 - x^10 - x^8 - x^6 - x^4 - x^2 = 1` (12-1-2-2-2-2)
`x^25 - x^12 - x^11 - x^10 - x^8 - x^6 - x^4 - x^2 = 1` (13-1-1-2-2-2-2)
`x^27 - x^14 - x^12 - x^11 - x^10 - x^8 - x^6 - x^4 - x^2 = 1` (13-[2]-1-1-2-2-2-2)
...

1.12724761986...
`x^10 - x^7 = 1` (3)
`x^13 - x^7 - x^3 = 1` (6-4)
`x^16 - x^7 - x^6 - x^3 = 1` (9-1-3)
`x^19 - x^9 - x^7 - x^6 - x^3 = 1` (10-2-1-3)
`x^21 - x^12 - x^9 - x^7 - x^6 - x^3 = 1` (11-[3]-2-1-3)
...

1.27857363379...
`x^6 - x^3 - x = 1` (3-2)
`x^11 - x^8 - x^5 - x^3 - x = 1` (3-[3-2]-2)
`x^16 - x^13 - x^10 - x^8 - x^5 - x^3 - x = 1` (3-3-2-3-2-2)
...

1.13045957186...
`x^10 - x^2 - x = 1` (8-1)
`x^19 - x^11 - x^9 - x^2 - x = 1` (8-[2-7]-1)
...

1.1347241384...
`x^6 - x = 1` (5)
`x^11 - x^5 - x = 1` (6-4)
`x^16 - x^10 - x^5 - x = 1` (6-[5]-4)
...

1.1357924646...
`x^13 - x^8 - x^3 = 1` (5-5)
`x^23 - x^18 - x^10 - x^8 - x^3 = 1` (5-[8-2]-5)
...

1.13685362751...
`x^10 - x^3 - x = 1` (7-2)
`x^19 - x^12 - x^9 - x^3 - x = 1` (7-[3-6]-2)
...

1.13715276855...
`x^13 - x^9 - x = 1` (4-8)
`x^25 - x^21 - x^12 - x^9 - x = 1` (4-[9-3]-8)
...

1.13951363652...
`x^12 - x^7 - x^2 = 1` (5-5)
`x^22 - x^17 - x^10 - x^7 - x^2 = 1` (5-[7-3]-5)
...

1.14132669997...
`x^13 - x^8 - x^4 = 1` (5-4)
`x^22 - x^17 - x^9 - x^8 - x^4 = 1` (5-[8-1]-4)
...

1.141685579...
`x^11 - x^9 = 1` (2)
`x^13 - x^9 - x^2 = 1` (4-7)
`x^15 - x^9 - x^4 - x^2 = 1` (6-5-2)
`x^17 - x^9 - x^6 - x^4 - x^2 = 1` (8-3-2-2)
`x^19 - x^9 - x^8 - x^6 - x^4 - x^2 = 1` (10-1-2-2-2)
`x^21 - x^10 - x^9 - x^8 - x^6 - x^4 - x^2 = 1` (11-1-1-2-2-2)
`x^23 - x^12 - x^10 - x^9 - x^8 - x^6 - x^4 - x^2 = 1` (11-[2]-1-1-2-2-2)
...

1.14377404488...
`x^11 - x^6 - x = 1` (5-5)
`x^21 - x^16 - x^10 - x^6 - x = 1` (5-[6-4]-5)
...

1.14510583258...
`x^12 - x^7 - x^3 = 1` (5-4)
`x^21 - x^16 - x^9 - x^7 - x^3 = 1` (5-[7-2]-4)
...

1.14567940223...
`x^12 - x^8 - x = 1` (4-7)
`x^23 - x^19 - x^11 - x^8 - x = 1` (4-[8-3]-7)
...

1.14613894965...
`x^8 - x^5 = 1` (3)
`x^11 - x^5 - x^3 = 1` (6-2)
`x^14 - x^6 - x^5 - x^3 = 1` (8-1-2)
`x^17 - x^9 - x^6 - x^5 - x^3 = 1` (8-[3]-1-2)
...

1.14811349735...
`x^9 - x^2 - x = 1` (7-1)
`x^17 - x^10 - x^8 - x^2 - x = 1` (7-[2-6]-1)
...

1.1512705749...
`x^13 - x^10 - x = 1` (3-9)
`x^25 - x^22 - x^12 - x^10 - x = 1` (3-[10-2]-9)
...

1.15559560581...
`x^11 - x^7 - x = 1` (4-6)
`x^21 - x^17 - x^10 - x^7 - x = 1` (4-[7-3]-6)
...

1.15615573116...
`x^11 - x^6 - x^3 = 1` (5-3)
`x^19 - x^14 - x^8 - x^6 - x^3 = 1` (5-[6-2]-3)
...

1.15660004786...
`x^9 - x^3 - x = 1` (6-2)
`x^17 - x^11 - x^8 - x^3 - x = 1` (6-[3-5]-2)
...

1.1585518931...
`x^7 - x^4 = 1` (3)
`x^10 - x^4 - x^3 = 1` (6-1)
`x^13 - x^6 - x^4 - x^3 = 1` (7-2-1)
`x^16 - x^9 - x^6 - x^4 - x^3 = 1` (7-[3]-2-1)
...

1.16086699653...
`x^12 - x^9 - x = 1` (3-8)
`x^23 - x^20 - x^11 - x^9 - x = 1` (3-[9-2]-8)
...

1.16185205478...
`x^9 - x^7 = 1` (2)
`x^11 - x^7 - x^2 = 1` (4-5)
`x^13 - x^7 - x^4 - x^2 = 1` (6-3-2)
`x^15 - x^7 - x^6 - x^4 - x^2 = 1` (8-1-2-2)
`x^17 - x^8 - x^7 - x^6 - x^4 - x^2 = 1` (9-1-1-2-2)
`x^19 - x^10 - x^8 - x^7 - x^6 - x^4 - x^2 = 1` (9-[2]-1-1-2-2)
...

1.16687648867...
`x^12 - x^9 - x^2 = 1` (3-7)
`x^22 - x^19 - x^10 - x^9 - x^2 = 1` (3-[9-1]-7)
...

1.16730397826...
`x^5 - x = 1` (4)
`x^9 - x^4 - x = 1` (5-3)
`x^13 - x^8 - x^4 - x = 1` (5-[4]-3)
...

or alternatively
`x^10 - x^6 - x = 1` (4-5)
`x^19 - x^15 - x^9 - x^6 - x = 1` (4-[6-3]-5)
...

1.16931139161...
`x^11 - x^7 - x^3 = 1` (4-4)
`x^19 - x^15 - x^8 - x^7 - x^3 = 1` (4-[7-1]-4)
...

1.16938136613...
`x^13 - x^9 - x^6 = 1` (4-3)
`x^20 - x^16 - x^9 - x^7 - x^6 = 1` (4-7-2-1)
`x^27 - x^23 - x^16 - x^14 - x^9 - x^7 - x^6 = 1` (4-7-2-[5-2]-1)
...

1.16953646999...
`x^10 - x^5 - x^3 = 1` (5-2)
`x^17 - x^12 - x^7 - x^5 - x^3 = 1` (5-[5-2]-2)
...

1.17132185638...
`x^8 - x^2 - x = 1` (6-1)
`x^15 - x^9 - x^7 - x^2 - x = 1` (6-[2-5]-1)
...

1.17203907904...
`x^11 - x^8 - x = 1` (3-7)
`x^21 - x^18 - x^10 - x^8 - x = 1` (3-[8-2]-7)
...

1.17295075002...
`x^13 - x^11 - x = 1` (2-10)
`x^25 - x^23 - x^12 - x^11 - x = 1` (2-[11-1]-10)
...

1.18138806405...
`x^9 - x^5 - x = 1` (4-4)
`x^17 - x^13 - x^8 - x^5 - x = 1` (4-[5-3]-4)
...

1.18312534771...
`x^8 - x^3 - x = 1` (5-2)
`x^15 - x^10 - x^7 - x^3 - x = 1` (5-[3-4]-2)
...

1.18427632235...
`x^12 - x^10 - x = 1` (2-9)
`x^23 - x^21 - x^11 - x^10 - x = 1` (2-[10-1]-9)
...

1.1852442447...
`x^10 - x^7 - x = 1` (3-6)
`x^19 - x^16 - x^9 - x^7 - x = 1` (3-[7-2]-6)
...

1.18616936991...
`x^9 - x^4 - x^3 = 1` (5-1)
`x^15 - x^10 - x^6 - x^4 - x^3 = 1` (5-[4-2]-1)
...

1.18636230734...
`x^13 - x^11 - x^3 = 1` (2-8)
`x^23 - x^21 - x^11 - x^10 - x^3 = 1` (2-10-1-7)
`x^33 - x^31 - x^21 - x^20 - x^11 - x^10 - x^3 = 1` (2-10-[1-9]-2-7)
...

1.18853068351...
`x^13 - x^10 - x^6 = 1` (3-4)
`x^20 - x^17 - x^10 - x^7 - x^6 = 1` (3-7-3-1)
`x^27 - x^24 - x^17 - x^14 - x^10 - x^7 - x^6 = 1` (3-7-[3-4]-3-1)
...

1.19071270708...
`x^7 - x^5 = 1` (2)
`x^9 - x^5 - x^2 = 1` (4-3)
`x^11 - x^5 - x^4 - x^2 = 1` (6-1-2)
`x^13 - x^6 - x^5 - x^4 - x^2 = 1` (7-1-1-2)
`x^15 - x^8 - x^6 - x^5 - x^4 - x^2 = 1` (7-[2]-1-1-2)
...

1.19385911132...
`x^5 - x^2 = 1` (3)
`x^8 - x^3 - x^2 = 1` (5-1)
`x^11 - x^6 - x^3 - x^2 = 1` (5-[3]-1)
...

1.19486649255...
`x^13 - x^9 - x^8 = 1` (4-1)
`x^18 - x^14 - x^9 - x^8 - x^5 = 1` (4-5-1-3)
`x^23 - x^19 - x^14 - x^10 - x^9 - x^8 - x^5 = 1` (4-5-[4-1]-1-3)
...

1.19504609972...
`x^13 - x^11 - x^4 = 1` (2-7)
`x^22 - x^20 - x^11 - x^9 - x^4 = 1` (2-9-2-5)
`x^31 - x^29 - x^20 - x^18 - x^11 - x^9 - x^4 = 1` (2-9-[2-7]-2-5)
...

1.19749143355...
`x^11 - x^9 - x = 1` (2-8)
`x^21 - x^19 - x^10 - x^9 - x = 1` (2-[9-1]-8)
...

1.19873093743...
`x^8 - x^4 - x = 1` (4-3)
`x^15 - x^11 - x^7 - x^4 - x = 1` (4-[4-3]-3)
...

1.20114522313...
`x^9 - x^6 - x = 1` (3-5)
`x^17 - x^14 - x^8 - x^6 - x = 1` (3-[6-2]-5)
...

1.20233022826...
`x^9 - x^5 - x^3 = 1` (4-2)
`x^15 - x^11 - x^6 - x^5 - x^3 = 1` (4-[5-1]-2)
...

1.20321603352...
`x^7 - x^2 - x = 1` (5-1)
`x^13 - x^8 - x^6 - x^2 - x = 1` (5-[2-4]-1)
...

1.21314972306...
`x^10 - x^8 - x = 1` (2-7)
`x^19 - x^17 - x^9 - x^8 - x = 1` (2-[8-1]-7)
...

1.22074408461...
`x^4 - x = 1` (3)
`x^7 - x^3 - x = 1` (4-2)
`x^10 - x^6 - x^3 - x = 1` (4-[3]-2)
...

or alternatively
`x^8 - x^5 - x = 1` (3-4)
`x^15 - x^12 - x^7 - x^5 - x = 1` (3-[5-2]-4)
...

1.23205463143...
`x^9 - x^7 - x = 1` (2-6)
`x^17 - x^15 - x^8 - x^7 - x = 1` (2-[7-1]-6)
`x^25 - x^23 - x^16 - x^15 - x^8 - x^7 - x = 1` (2-7-1-7-1-6)
...

1.23650570339...
`x^7 - x^3 - x^2 = 1` (4-1)
`x^12 - x^8 - x^5 - x^3 - x^2 = 1` (4-[3-2]-1)
`x^17 - x^13 - x^10 - x^8 - x^5 - x^3 - x^2 = 1` (4-3-2-3-2-1)
...

1.24564019063...
`x^7 - x^4 - x = 1` (3-3)
`x^13 - x^10 - x^6 - x^4 - x = 1` (3-[4-2]-3)
`x^19 - x^16 - x^12 - x^10 - x^6 - x^4 - x = 1` (3-4-2-4-2-3)
...

1.24985158886...
`x^6 - x^2 - x = 1` (4-1)
`x^11 - x^7 - x^5 - x^2 - x = 1` (4-[2-3]-1)
`x^16 - x^12 - x^10 - x^7 - x^5 - x^2 - x = 1` (4-2-3-2-3-1)
...

1.25542287108...
`x^8 - x^6 - x = 1` (2-5)
`x^15 - x^13 - x^7 - x^6 - x = 1` (2-[6-1]-5)
`x^22 - x^20 - x^14 - x^13 - x^7 - x^6 - x = 1` (2-6-1-6-1-5)
...

1.26373886081...
`x^7 - x^4 - x^2 = 1` (3-2)
`x^12 - x^9 - x^5 - x^4 - x^2 = 1` (3-[4-1]-2)
`x^17 - x^14 - x^10 - x^9 - x^5 - x^4 - x^2 = 1` (3-4-1-4-1-2)
...

1.26655954341...
`x^9 - x^6 - x^5 = 1` (3-1)
`x^13 - x^10 - x^6 - x^5 - x^4 = 1` (3-[4-1]-1)
...

1.27857363379...
`x^6 - x^3 - x = 1` (3-2)
`x^11 - x^8 - x^5 - x^3 - x = 1` (3-[3-2]-2)
`x^16 - x^13 - x^10 - x^8 - x^5 - x^3 - x = 1` (3-3-2-3-2-2)
...

1.28519903325...
`x^7 - x^5 - x = 1` (2-4)
`x^13 - x^11 - x^6 - x^5 - x = 1` (2-[5-1]-4)
`x^19 - x^17 - x^12 - x^11 - x^6 - x^5 - x = 1` (2-5-1-5-1-4)
...

1.3247179572... (Plastic)
`x^5 - x^2 - x = 1` (3-1)
`x^9 - x^6 - x^4 - x^2 - x = 1` (3-[2-2]-1)
`x^13 - x^10 - x^8 - x^6 - x^4 - x^2 - x = 1` (3-2-2-2-2-1)
`x^17 - x^14 - x^12 - x^10 - x^8 - x^6 - x^4 - x^2 - x = 1` (3-2-2-2-2-2-2-1)
...

1.37108552626...
`x^8 - x^6 - x^5 = 1` (2-1)
`x^11 - x^9 - x^6 - x^5 - x^3 = 1` (2-[3-1]-2)
...

1.3802775691...
`x^5 - x^3 - x = 1` (2-2)
`x^9 - x^7 - x^4 - x^3 - x = 1` (2-[3-1]-2)
`x^13 - x^11 - x^8 - x^7 - x^4 - x^3 - x = 1` (2-3-1-3-1-2)
...

1.38500505355...
`x^7 - x^5 - x^4 = 1` (2-1)
`x^10 - x^8 - x^5 - x^4 - x^3 = 1` (2-3-1-1)
`x^13 - x^11 - x^8 - x^6 - x^5 - x^4 - x^3 = 1` (2-3-[2-1]-1-1)
`x^16 - x^14 - x^11 - x^9 - x^8 - x^6 - x^5 - x^4 - x^3 = 1` (2-3-2-1-2-1-1-1)
...

1.44326879127...
`x^7 - x^6 - x^3 = 1` (1-3)
`x^11 - x^10 - x^6 - x^4 - x^3 = 1` (1-4-2-1)
`x^15 - x^14 - x^10 - x^8 - x^6 - x^4 - x^3 = 1` (1-4-2-[2-2]-1)
`x^19 - x^18 - x^14 - x^12 - x^10 - x^8 - x^6 - x^4 - x^3 = 1` (1-4-2-2-2-2-2-1)
...

1.46557123188...
`x^4 - x^2 - x = 1` (2-1)
`x^7 - x^5 - x^3 - x^2 - x = 1` (2-[2-1]-1)
`x^10 - x^8 - x^6 - x^5 - x^3 - x^2 - x = 1` (2-2-1-2-1-1)
`x^13 - x^11 - x^9 - x^8 - x^6 - x^5 - x^3 - x^2 - x = 1` (2-2-1-2-1-2-1-1)
...

1.47792980435...
`x^11 - x^10 - x^8 = 1` (1-2)
`x^14 - x^13 - x^10 - x^8 - x^3 = 1` (1-3-2-5)
`x^17 - x^16 - x^13 - x^10 - x^8 - x^6 - x^3 = 1` (1-3-3-2-2-3)
`x^20 - x^19 - x^16 - x^13 - x^10 - x^9 - x^8 - x^6 - x^3 = 1` (1-3-3-3-1-1-2-3)
...

1.50159480354...
`x^8 - x^7 - x^5 = 1` (1-2)
`x^11 - x^10 - x^7 - x^5 - x^3 = 1` (1-[3-2]-2)
`x^14 - x^13 - x^10 - x^7 - x^6 - x^5 - x^3 = 1` (1-3-3-1-1-2)
`x^17 - x^16 - x^13 - x^10 - x^9 - x^7 - x^6 - x^5 - x^3 = 1` (1-3-3-1-[2-1]-1-2)
`x^20 - x^19 - x^16 - x^13 - x^12 - x^10 - x^9 - x^7 - x^6 - x^5 - x^3 = 1` (1-3-3-1-2-1-2-1-1-2)
...

1.53849659221...
`x^6 - x^5 - x^3` (1-2)
`x^12 - x^11 - x^9 - x^5 - x^3 = 1` (1-[2-4]-2)
`x^18 - x^17 - x^15 - x^11 - x^9 - x^5 - x^3 = 1` (1-2-4-2-4-2)
...

1.5701473122...
`x^5 - x^4 - x^2` (1-2)
`x^8 - x^7 - x^4 - x^3 - x^2 = 1` (1-3-1-1)
`x^11 - x^10 - x^7 - x^6 - x^4 - x^3 - x^2 = 1` (1-3-[1-2]-1-1)
...

1.61803398875... (Phi)
`x^2 - x = 1` (1)
`x^4 - x^3 - x = 1` (1-2)
`x^6 - x^5 - x^3 - x = 1` (1-2-2)
`x^8 - x^7 - x^5 - x^3 - x = 1` (1-2-2-2)
`x^10 - x^9 - x^7 - x^5 - x^3 - x = 1` (1-2-2-2-2)
`x^12 - x^11 - x^9 - x^7 - x^5 - x^3 - x = 1` (1-2-2-2-2-2)
...

1.70490277604...
`x^5 - x^4 - x^3 = 1` (1-1)
`x^10 - x^9 - x^8 - x^4 - x^3 = 1` (1-[1-4]-1)
`x^15 - x^14 - x^13 - x^9 - x^8 - x^4 - x^3 = 1` (1-1-4-1-4-1)
...

1.83928675521... (Tribonacci)
`x^3 - x^2 - x = 1` (1-1)
`x^6 - x^5 - x^4 - x^2 - x = 1` (1-[1-2]-1)
`x^9 - x^8 - x^7 - x^5 - x^4 - x^2 - x = 1` (1-1-2-1-2-1)
`x^12 - x^11 - x^10 - x^8 - x^7 - x^5 - x^4 - x^2 - x = 1` (1-1-2-1-2-1-2-1)
`x^15 - x^14 - x^13 - x^11 - x^10 - x^8 - x^7 - x^5 - x^4 - x^2 - x = 1` (1-1-2-1-2-1-2-1-2-1)
`x^18 - x^17 - x^16 - x^14 - x^13 - x^12 - x^11 - x^10 - x^8 - x^7 - x^5 - x^4 - x^2 - x = 1` (1-1-2-1-2-1-2-1-2-1-2-1)
...

1.92756197548... (Tetranacci)
`x^4 - x^3 - x^2 - x = 1` (1-1-1)
`x^8 - x^7 - x^6 - x^5 - x^3 - x^2 - x = 1` (1-1-[1-2-1]-1)
`x^12 - x^11 - x^10 - x^9 - x^7 - x^6 - x^5 - x^3 - x^2 - x = 1` (1-1-1-2-1-1-2-1-1)
`x^16 - x^15 - x^14 - x^13 - x^11 - x^10 - x^9 - x^7 - x^6 - x^5 - x^3 - x^2 - x = 1` (1-1-1-2-1-1-2-1-1-2-1-1)
...

1.96594823665... (Pentanacci)
`x^5 - x^4 - x^3 - x^2 - x = 1` (1-1-1-1)
`x^10 - x^9 - x^8 - x^7 - x^6 - x^4 - x^3 - x^2 - x = 1` (1-1-[1-1-2-1]-1-1)
`x^15 - x^14 - x^13 - x^12 - x^11 - x^9 - x^8 - x^7 - x^6 - x^4 - x^3 - x^2 - x = 1`
`x^20 - x^19 - x^18 - x^17 - x^16 - x^14 - x^13 - x^12 - x^11 - x^9 - x^8 - x^7 - x^6 - x^4 - x^3 - x^2 - x = 1`
...

1.98358284342... (Hexanacci)
`x^6 - x^5 - x^4 - x^3 - x^2 - x = 1` (1-1-1-1-1)
`x^12 - x^11 - x^10 - x^9 - x^8 - x^7 - x^5 - x^4 - x^3 - x^2 - x = 1` (1-1-1-[1-1-2-1-1]-1-1)
`x^18 - x^17 - x^16 - x^15 - x^14 - x^13 - x^11 - x^10 - x^9 - x^8 - x^7 - x^5 - x^4 - x^3 - x^2 - x = 1`
...

1.9919641966... (Heptanacci)
`x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x = 1` (1-1-1-1-1-1)
`x^14 - x^13 - x^12 - x^11 - x^10 - x^9 - x^8 - x^6 - x^5 - x^4 - x^3 - x^2 - x = 1` (1-1-1-[1-1-1-2-1-1]-1-1-1)
...

1.99603117974... (Octanacci)
`x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x = 1` (1-1-1-1-1-1-1)
`x^16 - x^15 - x^14 - x^13 - x^12 - x^11 - x^10 - x^9 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x = 1` (1-1-1-1-[1-1-1-2-1-1-1]-1-1-1)
...

1.99802947026... (Nonanacci)
`x^9 - x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x = 1` (1-1-1-1-1-1-1-1)
`x^18 - x^17 - x^16 - x^15 - x^14 - x^13 - x^12 - x^11 - x^10 - x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x = 1` (1-1-1-1-[1-1-1-1-2-1-1-1]-1-1-1-1)
...

1.99901863271... (Decanacci)
`x^10 - x^9 - x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x = 1` (1-1-1-1-1-1-1-1-1)
`x^20 - x^19 - x^18 - x^17 - x^16 - x^15 - x^14 - x^13 - x^12 - x^11 - x^9 - x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x = 1` (1-1-1-1-1-[1-1-1-1-2-1-1-1-1]-1-1-1-1)
...

1.99951040198... (Undecanacci)
`x^11 - x^10 - x^9 - x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x = 1` (1-1-1-1-1-1-1-1-1-1)
`x^22 - x^21 - x^20 - x^19 - x^18 - x^17 - x^16 - x^15 - x^14 - x^13 - x^12 - x^10 - x^9 - x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x = 1` (1-1-1-1-1-[1-1-1-1-1-2-1-1-1-1]-1-1-1-1-1)
...

1.99975550094... (Dodecanacci)
`x^12 - x^11 - x^10 - x^9 - x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x = 1` (1-1-1-1-1-1-1-1-1-1-1)
`x^24 - x^23 - x^22 - x^21 - x^20 - x^19 - x^18 - x^17 - x^16 - x^15 - x^14 - x^13 - x^11 - x^10 - x^9 - x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x = 1` (1-1-1-1-1-1-[1-1-1-1-1-2-1-1-1-1-1]-1-1-1-1-1)
...

1.99987783271... (Tredecanacci)
`x^13 - x^12 - x^11 - x^10 - x^9 - x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x = 1` (1-1-1-1-1-1-1-1-1-1-1-1)
`x^26 - x^25 - x^24 - x^23 - x^22 - x^21 - x^20 - x^19 - x^18 - x^17 - x^16 - x^15 - x^14 - x^12 - x^11 - x^10 - x^9 - x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x = 1` (1-1-1-1-1-1-[1-1-1-1-1-1-2-1-1-1-1-1]-1-1-1-1-1-1)
...