A214031 - OEIS

A214031

Fixed points of A214030.

13, 19, 23, 37, 41, 47, 89, 139, 157, 211, 277, 281, 331, 373, 379, 397, 499, 503, 521, 571, 613, 619, 641, 647, 691, 733, 739, 743, 757, 761, 811, 853, 859, 863, 877, 983, 997, 1051, 1093, 1103, 1117, 1171, 1213, 1223, 1237, 1289, 1297, 1409, 1453, 1459, 1481, 1487

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OFFSET

1,1

COMMENTS

This sequence is to A214030 as A000057 is to A001177. It would be nice to have an interpretation of this sequence akin to the interpretation of A000057 as the set of primes which divide all Fibonacci sequences, having arbitrary initial values for a(1),a(2). The linearly recursive sequence which seems to be associated to this is 3*f(n) = 6*f(n-1) + 2*f(n-2), but this does not have integral values.

If we use the sequence 3,2,3,2,3,2,... instead of 2,3,2,3,... we end up with the same sequence a(n).

LINKS

Table of n, a(n) for n=1..52.

FORMULA

{n: A214030(n)=n}.

PROG

(PARI)

{b23(n)=local(t, m=1, s=[n]); if (n<2, 0, while(1,

if(m%2, s=concat(s, 2), s=concat(s, 3));

t=contfracpnqn(concat(s, n));

t=contfrac(n*t[1, 1]/t[2, 1]);

if(t[1]<n^2||t[#t]<n^2, m++, break)); m)};