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A105935 Indices of Lucas 7-step numbers A104621 which have a nontrivial divisor in common with index. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 18 03:02 EST 2022. Contains 350410 sequences. (Running on oeis4.)