A261311 Fixed points of sequence A262211 which yields the minimum number of 12's such that [n; 12, ..., 12, n] = [x; ..., x] for some x; [...] being continued fractions.

19, 23, 31, 43, 59, 79, 103, 163, 179, 199, 227, 239, 251, 283, 331, 347, 383, 431, 439, 463, 467, 479, 487, 499, 523, 547, 587, 607, 631, 647, 683, 727, 827, 883, 907, 911, 919, 967, 991, 1019, 1031, 1051, 1087, 1123, 1171, 1303, 1327, 1423, 1499, 1511, 1523, 1531, 1567, 1571, 1667

Offset

1,1

Comments

Surprisingly, the variant A213900 with 11 instead of 12 has the same fixed points A000057 as the variant with 1 instead of 12, but other variants (A262212 - A262220 and A262211) have different sets of fixed points (A213891 - A213899 and this).

Links

Table of n, a(n) for n=1..55.

Mathematica

f[m_, n_] := Block[{c, k = 1}, c[x_, y_] := ContinuedFraction[x FromContinuedFraction[Join[{x}, Table[m, {y}], {x}]]]; While[First@ c[n, k] != Last@ c[n, k], k++]; k]; Select[Range[2, 1000], f[12, #] == # &] (* Michael De Vlieger, Sep 16 2015 *)

Prog

(PARI) for(n=2, 9999, n==A262211(n)&&print1(n", "))

Crossrefs

Cf. A213648, A262212 - A262220, A213900, A262211; A000057, A213891 - A213899.

Sequence in context: A019360 A269666 A007639 * A168144 A108271 A351121

Adjacent sequences: A261308 A261309 A261310 * A261312 A261313 A261314

Keyword

nonn

Author

M. F. Hasler, Sep 15 2015

Status

approved