A105285 Indices of Lucas 3-step numbers A001644 which have a nontrivial divisor in common with index.

6, 15, 18, 21, 35, 39, 44, 45, 54, 55, 57, 78, 80, 84, 90, 93, 96, 117, 120, 123, 132, 133, 135, 140, 147, 154, 156, 162, 171, 174, 195, 201, 210, 213, 234, 235, 240, 245, 247, 249, 252, 259, 264, 273, 275, 279, 286, 288, 290, 291, 295, 299, 312, 318, 323, 327

Offset

1,1

Comments

Extension by T. D. Noe. Wanted: closed-form formula for this as exists for Fibonacci and Lucas numbers. See also A105762 (prime Lucas 3-step numbers).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

gcd(a(n), A001644(a(n))) > 1.

Example

gcd(6, A001644(6)) = gcd(6,39) = 3,
gcd(21, A001644(21)) = gcd(21,361109) = 7.

Mathematica

m=300; s = LinearRecurrence[{1, 1, 1}, {3, 1, 3}, m+1]; Select[Range[m], !CoprimeQ[#, s[[#+1]]] &] (* Amiram Eldar, Sep 05 2019 *)

Crossrefs

Cf. A001644, A104714, A105762.

Sequence in context: A302296 A070999 A128693 * A138922 A362141 A044058

Adjacent sequences: A105282 A105283 A105284 * A105286 A105287 A105288

Keyword

easy,nonn

Author

Jonathan Vos Post, Apr 25 2005

Extensions

More terms from Amiram Eldar, Sep 05 2019

Status

approved