

A105285


Indices of Lucas 3step numbers A001644 which have a nontrivial divisor in common with index.


2



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
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OFFSET

1,1


COMMENTS

Extension by T. D. Noe. Wanted: closedform formula for this as exists for Fibonacci and Lucas numbers. See also A105762 (prime Lucas 3step numbers).


LINKS

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


FORMULA

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


EXAMPLE

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


MATHEMATICA

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


CROSSREFS

Cf. A001644, A104714, A105762.
Sequence in context: A302296 A070999 A128693 * A138922 A044058 A105139
Adjacent sequences: A105282 A105283 A105284 * A105286 A105287 A105288


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Apr 25 2005


EXTENSIONS

More terms from Amiram Eldar, Sep 05 2019


STATUS

approved



