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

Author

Jonathan Vos Post, Apr 25 2005

Keywords

• easy
• nonn

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).

Examples

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

Links

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

Crossrefs

Cf. A001644, A104714, A105762.

Programs

Mathematica

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

Formula

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

Extensions

More terms from Amiram Eldar, Sep 05 2019