cp's OEIS Frontend

A309585 Numbers k with 4 zeros in a fundamental period of A000129 mod k.

%I A309585 #17 Jun 17 2024 10:50:06
%S A309585 5,13,25,29,37,53,61,65,101,109,125,137,145,149,157,169,173,181,185,
%T A309585 197,229,265,269,277,293,305,317,325,349,373,377,389,397,421,461,481,
%U A309585 505,509,521,541,545,557,569,593,613,625,653,661,677,685,689,701,709
%N A309585 Numbers k with 4 zeros in a fundamental period of A000129 mod k.
%C A309585 Numbers k such that A214027(k) = 4.
%C A309585 Also numbers k such that A214028(k) is odd.
%H A309585 Jianing Song, <a href="/A309585/b309585.txt">Table of n, a(n) for n = 1..1000</a>
%o A309585 (PARI) for(k=1, 700, if(A214027(k)==4, print1(k, ", ")))
%Y A309585 Cf. A214028.
%Y A309585 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 A309585                              |   m=1    |   m=2    |   m=3
%Y A309585 -----------------------------+----------+----------+---------
%Y A309585 The sequence {x(n)}          | A000045  | A000129  | A006190
%Y A309585 The sequence {w(k)}          | A001176  | A214027  | A322906
%Y A309585 Primes p such that w(p) = 1  | A112860* | A309580  | A309586
%Y A309585 Primes p such that w(p) = 2  | A053027  | A309581  | A309587
%Y A309585 Primes p such that w(p) = 4  | A053028  | A261580  | A309588
%Y A309585 Numbers k such that w(k) = 1 | A053031  | A309583  | A309591
%Y A309585 Numbers k such that w(k) = 2 | A053030  | A309584  | A309592
%Y A309585 Numbers k such that w(k) = 4 | A053029  | this seq | A309593
%Y A309585 * and also A053032 U {2}
%K A309585 nonn
%O A309585 1,1
%A A309585 _Jianing Song_, Aug 10 2019