A309585 Numbers k with 4 zeros in a fundamental period of A000129 mod k.

5, 13, 25, 29, 37, 53, 61, 65, 101, 109, 125, 137, 145, 149, 157, 169, 173, 181, 185, 197, 229, 265, 269, 277, 293, 305, 317, 325, 349, 373, 377, 389, 397, 421, 461, 481, 505, 509, 521, 541, 545, 557, 569, 593, 613, 625, 653, 661, 677, 685, 689, 701, 709

Offset: 1

Author

Jianing Song, Aug 10 2019

Keywords

• nonn

Comments

Numbers k such that A214027(k) = 4.

Also numbers k such that A214028(k) is odd.

Links

• Jianing Song, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. 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 | A309584 | A309592

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

* and also A053032 U {2}

Programs

PARI

for(k=1, 700, if(A214027(k)==4, print1(k, ", ")))