cp's OEIS Frontend

A309593 Numbers k with 4 zeros in a fundamental period of A006190 mod k.

%I A309593 #16 Jun 17 2024 10:50:14
%S A309593 5,10,13,25,26,29,37,41,50,58,65,73,74,82,89,97,109,125,130,137,145,
%T A309593 146,149,157,169,178,181,185,193,194,197,205,218,229,233,241,250,269,
%U A309593 274,281,290,293,298,314,317,325,338,349,353,362,365,370,373,377
%N A309593 Numbers k with 4 zeros in a fundamental period of A006190 mod k.
%C A309593 Numbers k such that A322906(k) = 4.
%C A309593 Also numbers k such that A214027(k) is odd.
%H A309593 Jianing Song, <a href="/A309593/b309593.txt">Table of n, a(n) for n = 1..2000</a>
%o A309593 (PARI) for(k=1, 400, if(A322906(k)==4, print1(k, ", ")))
%Y A309593 Cf. A322907.
%Y A309593 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 A309593                              |   m=1    |   m=2   |   m=3
%Y A309593 -----------------------------+----------+---------+----------
%Y A309593 The sequence {x(n)}          | A000045  | A000129 | A006190
%Y A309593 The sequence {w(k)}          | A001176  | A214027 | A322906
%Y A309593 Primes p such that w(p) = 1  | A112860* | A309580 | A309586
%Y A309593 Primes p such that w(p) = 2  | A053027  | A309581 | A309587
%Y A309593 Primes p such that w(p) = 4  | A053028  | A261580 | A309588
%Y A309593 Numbers k such that w(k) = 1 | A053031  | A309583 | A309591
%Y A309593 Numbers k such that w(k) = 2 | A053030  | A309584 | A309592
%Y A309593 Numbers k such that w(k) = 4 | A053029  | A309585 | this seq
%Y A309593 * and also A053032 U {2}
%K A309593 nonn
%O A309593 1,1
%A A309593 _Jianing Song_, Aug 10 2019