

A105935


Indices of Lucas 7step 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
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OFFSET

1,1


COMMENTS

Wanted: closedform formula for this as exists for Fibonacci and Lucas numbers. Lucas 7step numbers also known as heptanacciLucas numbers. The prime Lucas 7step 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



