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 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
 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 (list; graph; refs; listen; history; text; internal format)
 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 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 A245585 Adjacent sequences:  A261308 A261309 A261310 * A261312 A261313 A261314 KEYWORD nonn AUTHOR M. F. Hasler, Sep 15 2015 STATUS approved

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Last modified February 20 07:28 EST 2020. Contains 332067 sequences. (Running on oeis4.)