A309583 Numbers k with 1 zero in a fundamental period of A000129 mod k.

1, 2, 4, 7, 8, 14, 16, 20, 23, 24, 28, 31, 32, 40, 41, 46, 47, 48, 49, 52, 56, 62, 64, 71, 72, 79, 80, 82, 88, 92, 94, 96, 98, 100, 103, 104, 112, 116, 120, 124, 127, 128, 140, 142, 144, 148, 151, 152, 158, 160, 161, 164, 167, 168, 176, 184, 188, 191, 192

Offset: 1

Author

Jianing Song, Aug 10 2019

Keywords

• nonn

Comments

Numbers k such that A214027(k) = 1.

The odd numbers k satisfy A175181(k) == 2 (mod 4).

Links

• Jianing Song, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A175181.

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 | this seq | A309591

Numbers k such that w(k) = 2 | A053030 | A309584 | A309592

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

* and also A053032 U {2}

Programs

PARI

for(k=1, 200, if(A214027(k)==1, print1(k, ", ")))