cp's OEIS Frontend

A309584 Numbers k with 2 zeros in a fundamental period of A000129 mod k.

%I A309584 #21 Jun 17 2024 10:50:01
%S A309584 3,6,9,10,11,12,15,17,18,19,21,22,26,27,30,33,34,35,36,38,39,42,43,44,
%T A309584 45,50,51,54,55,57,58,59,60,63,66,67,68,69,70,73,74,75,76,77,78,81,83,
%U A309584 84,85,86,87,89,90,91,93,95,97,99,102,105,106,107,108,110
%N A309584 Numbers k with 2 zeros in a fundamental period of A000129 mod k.
%C A309584 Numbers k such that A214027(k) = 2.
%C A309584 This sequence contains all numbers k such that 4 divides A214028(k). As a consequence, this sequence contains all numbers congruent to 3 modulo 8.
%C A309584 This sequence contains all odd numbers k such that 8 divides A175181(k).
%H A309584 Jianing Song, <a href="/A309584/b309584.txt">Table of n, a(n) for n = 1..10000</a>
%o A309584 (PARI) for(k=1, 100, if(A214027(k)==2, print1(k, ", ")))
%Y A309584 Cf. A175181, A214028.
%Y A309584 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 A309584                              |   m=1    |   m=2    |   m=3
%Y A309584 -----------------------------+----------+----------+---------
%Y A309584 The sequence {x(n)}          | A000045  | A000129  | A006190
%Y A309584 The sequence {w(k)}          | A001176  | A214027  | A322906
%Y A309584 Primes p such that w(p) = 1  | A112860* | A309580  | A309586
%Y A309584 Primes p such that w(p) = 2  | A053027  | A309581  | A309587
%Y A309584 Primes p such that w(p) = 4  | A053028  | A261580  | A309588
%Y A309584 Numbers k such that w(k) = 1 | A053031  | A309583  | A309591
%Y A309584 Numbers k such that w(k) = 2 | A053030  | this seq | A309592
%Y A309584 Numbers k such that w(k) = 4 | A053029  | A309585  | A309593
%Y A309584 * and also A053032 U {2}
%K A309584 nonn
%O A309584 1,1
%A A309584 _Jianing Song_, Aug 10 2019