A105935 - OEIS

%I #8 Sep 05 2019 11:23:09

%S 6,12,18,20,21,33,36,42,54,57,60,65,87,93,99,100,104,105,108,111,141,

%T 147,152,153,155,156,162,165,171,177,180,189,192,195,210,215,220,222,

%U 230,235,238,240,249,255,261,264,273,276,279,280,286,294,295,297,300

%N Indices of Lucas 7-step numbers A104621 which have a nontrivial divisor in common with index.

%C 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.

%H Amiram Eldar, <a href="/A105935/b105935.txt">Table of n, a(n) for n = 1..10000</a>

%F gcd(a(n), A104621(a(n))) > 1.

%e gcd(a(n), A104621(6,12,18,33,36,57,60,87,93,108)) = 3,

%e gcd(a(n), A104621(20,65,100,105)) = 5,

%e gcd(a(n), A104621(21,42)) = 7,

%e gcd(a(n), A104621(54,99)) = 9,

%e gcd(a(n), A104621(104)) = 13.

%t 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 *)

%Y Cf. A104621, A105285, A105289.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Apr 26 2005

%E Offset corrected and a(5)-a(6) and more terms added by _Amiram Eldar_, Sep 05 2019