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%I #14 Feb 19 2021 12:37:33
%S 5,13,25,29,37,53,61,65,101,109,125,137,145,149,157,169,173,181,185,
%T 197,229,265,269,277,293,305,317,325,349,373,377,389,397,421,461,481,
%U 505,509,521,541,545,557,569,593,613,625,653,661,677,685,689,701,709
%N Numbers k with 4 zeros in a fundamental period of A000129 mod k.
%C Numbers k such that A214027(k) = 4.
%C Also numbers k such that A214028(k) is odd.
%H Jianing Song, <a href="/A309585/b309585.txt">Table of n, a(n) for n = 1..1000</a>
%o (PARI) for(k=1, 700, if(A214027(k)==4, print1(k, ", ")))
%Y Cf. A000129, A214027, A214028.
%Y Let {x(n)} be a sequence defined by x(0) = 0, x(1) = 1, x(n+2) = m*x(n+1) + x(n). Let w(k) be the number of zeros in a fundamental period of {x(n)} modulo k.
%Y | m=1 | m=2 | m=3
%Y Primes p such that w(p) = 1 | A112860* | A309580 | A309586
%Y Primes p such that w(p) = 2 | A053027 | A309581 | A309587
%Y Primes p such that w(p) = 4 | A053028 | A261580 | A309588
%Y Numbers k such that w(k) = 1 | A053031 | A309583 | A309591
%Y Numbers k such that w(k) = 2 | A053030 | A309584 | A309592
%Y Numbers k such that w(k) = 4 | A053029 | this seq | A309593
%Y * and also A053032 U {2}
%K nonn
%O 1,1
%A _Jianing Song_, Aug 10 2019
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