A309592 Numbers k with 2 zeros in a fundamental period of A006190 mod k.

7, 8, 11, 14, 15, 16, 17, 19, 20, 21, 22, 24, 28, 30, 31, 32, 33, 34, 35, 38, 39, 40, 42, 44, 45, 47, 48, 49, 51, 52, 55, 56, 57, 59, 60, 62, 63, 64, 66, 67, 68, 70, 71, 72, 75, 76, 77, 78, 80, 83, 84, 85, 87, 88, 90, 91, 93, 94, 95, 96, 98, 99, 100, 102, 104

Offset: 1

Author

Jianing Song, Aug 10 2019

Keywords

• nonn

Comments

Numbers k such that A322906(k) = 2.

This sequence contains all numbers k such that 4 divides A322907(k). As a consequence, this sequence contains all numbers congruent to 7, 11, 15, 19, 31, 47 modulo 52.

This sequence contains all odd numbers k such that 8 divides A175182(k).

Links

• Jianing Song, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A175182, A322907.

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.

| m=1 | m=2 | m=3

-----------------------------+----------+---------+----------

The sequence {x(n)} | A000045 | A000129 | A006190

The sequence {w(k)} | A001176 | A214027 | A322906

Primes p such that w(p) = 1 | A112860* | A309580 | A309586

Primes p such that w(p) = 2 | A053027 | A309581 | A309587

Primes p such that w(p) = 4 | A053028 | A261580 | A309588

Numbers k such that w(k) = 1 | A053031 | A309583 | A309591

Numbers k such that w(k) = 2 | A053030 | A309584 | this seq

Numbers k such that w(k) = 4 | A053029 | A309585 | A309593

* and also A053032 U {2}

Programs

PARI

for(k=1, 100, if(A322906(k)==2, print1(k, ", ")))