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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
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
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
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