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

3, 6, 9, 10, 11, 12, 15, 17, 18, 19, 21, 22, 26, 27, 30, 33, 34, 35, 36, 38, 39, 42, 43, 44, 45, 50, 51, 54, 55, 57, 58, 59, 60, 63, 66, 67, 68, 69, 70, 73, 74, 75, 76, 77, 78, 81, 83, 84, 85, 86, 87, 89, 90, 91, 93, 95, 97, 99, 102, 105, 106, 107, 108, 110

Offset: 1

Author

Jianing Song, Aug 10 2019

Keywords

• nonn

Comments

Numbers k such that A214027(k) = 2.

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.

This sequence contains all odd numbers k such that 8 divides A175181(k).

Links

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

Crossrefs

Cf. A175181, A214028.

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 | this seq | A309592

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

* and also A053032 U {2}

Programs

PARI

for(k=1, 100, if(A214027(k)==2, print1(k, ", ")))