A105935 Indices of Lucas 7-step numbers A104621 which have a nontrivial divisor in common with index.

6, 12, 18, 20, 21, 33, 36, 42, 54, 57, 60, 65, 87, 93, 99, 100, 104, 105, 108, 111, 141, 147, 152, 153, 155, 156, 162, 165, 171, 177, 180, 189, 192, 195, 210, 215, 220, 222, 230, 235, 238, 240, 249, 255, 261, 264, 273, 276, 279, 280, 286, 294, 295, 297, 300

Offset

1,1

Comments

Wanted: closed-form formula for this as exists for Fibonacci and Lucas numbers. Lucas 7-step numbers also known as heptanacci-Lucas numbers. The prime Lucas 7-step numbers are A105768, their indices being A104622.

Links

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

Formula

gcd(a(n), A104621(a(n))) > 1.

Example

gcd(a(n), A104621(6,12,18,33,36,57,60,87,93,108)) = 3,
gcd(a(n), A104621(20,65,100,105)) = 5,
gcd(a(n), A104621(21,42)) = 7,
gcd(a(n), A104621(54,99)) = 9,
gcd(a(n), A104621(104)) = 13.

Mathematica

m=300; s = LinearRecurrence[{1, 1, 1, 1, 1, 1, 1}, {7, 1, 3, 7, 15, 31, 63}, m+1]; Select[Range[m], !CoprimeQ[#, s[[#+1]]] &] (* Amiram Eldar, Sep 05 2019 *)

Crossrefs

Cf. A104621, A105285, A105289.

Sequence in context: A315722 A343126 A049094 * A105289 A328608 A328671

Adjacent sequences: A105932 A105933 A105934 * A105936 A105937 A105938

Keyword

easy,nonn

Author

Jonathan Vos Post, Apr 26 2005

Extensions

Offset corrected and a(5)-a(6) and more terms added by Amiram Eldar, Sep 05 2019

Status

approved