A309583 - OEIS

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

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OFFSET

1,2

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

PROG

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

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}

Sequence in context: A353441 A004616 A322386 * A327478 A062846 A102824

Adjacent sequences: A309580 A309581 A309582 * A309584 A309585 A309586

KEYWORD

nonn

AUTHOR

Jianing Song, Aug 10 2019

STATUS

approved