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

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)};
To print the sequence A214031(n) to the screen,
for(i=1, 500, if(b23(i)==i, print1(i, ", ")));

Crossrefs

Cf. A000057, A001177, A214030.

Sequence in context: A257590 A121877 A109902 * A250293 A058898 A227092

Adjacent sequences: A214028 A214029 A214030 * A214032 A214033 A214034

Keyword

nonn

Author

Art DuPre, Jul 12 2012

Status

approved