A105764 -id:A105764 - cp's OEIS frontend

A105289 Indices of Lucas 5-step numbers A074048 which have a nontrivial divisor in common with index.

6, 12, 18, 20, 21, 33, 36, 48, 51, 54, 55, 60, 75, 78, 87, 99, 100, 108, 110, 112, 114, 120, 129, 132, 133, 144, 147, 153, 154, 155, 159, 162, 165, 174, 177, 180, 182, 183, 185, 195, 210, 219, 225, 228, 230, 234, 237, 245, 261, 267, 270, 275, 285, 290, 297, 310

Offset: 1

Jonathan Vos Post, Apr 25 2005

Extension by T. D. Noe. Wanted: closed-form formula for this as exists for Fibonacci and Lucas numbers. See also A105764 (indices of prime Lucas 5-step numbers).

			gcd(6, A074048(6)) = gcd(6,57) = 3,
gcd(20, A074048(20)) = gcd(20,743775) = 5.
gcd(21, A074048(21)) = gcd(21,1462223) = 7.

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

Cf. A074048, A104714, A105764.

m=300; s = LinearRecurrence[{1, 1, 1, 1, 1}, {5, 1, 3, 7, 15}, m+1]; Select[Range[m], !CoprimeQ[#, s[[#+1]]] &] (* Amiram Eldar, Sep 05 2019 *)

gcd(a(n), A074048(a(n))) > 1.

More terms from Amiram Eldar, Sep 05 2019

A105765 Prime Lucas 5-step numbers, A074048.

Original entry on oeis.org

3, 7, 31, 113, 223, 439, 863, 6553, 641449337, 18837477823, 40276345611255837298559, 58893004546665606516457357571, 9774215601155945008361439560567878777

Offset: 1

T. D. Noe, Apr 22 2005

nonn

Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4
Eric Weisstein's World of Mathematics, Lucas n-Step Number

Cf. A105764 (indices of prime Lucas 5-step numbers).

a={-1, -1, -1, -1, 5}; lst={}; Do[s=Plus@@a; a=RotateLeft[a]; a[[ -1]]=s; If[PrimeQ[s], AppendTo[lst, s]], {n, 1000}]; lst

cp's OEIS Frontend

A105289 Indices of Lucas 5-step numbers A074048 which have a nontrivial divisor in common with index.

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