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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.

%I A261311 #12 Sep 22 2015 16:42:57
%S A261311 19,23,31,43,59,79,103,163,179,199,227,239,251,283,331,347,383,431,
%T A261311 439,463,467,479,487,499,523,547,587,607,631,647,683,727,827,883,907,
%U A261311 911,919,967,991,1019,1031,1051,1087,1123,1171,1303,1327,1423,1499,1511,1523,1531,1567,1571,1667
%N 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.
%C A261311 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).
%t A261311 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 *)
%o A261311 (PARI) for(n=2,9999,n==A262211(n)&&print1(n","))
%Y A261311 Cf. A213648, A262212 - A262220, A213900, A262211; A000057, A213891 - A213899.
%K A261311 nonn
%O A261311 1,1
%A A261311 _M. F. Hasler_, Sep 15 2015