A256559 a(n) = A256557(n)/A166133(n+1), n>=3.

5, 1, 9, 8, 7, 2, 13, 12, 11, 5, 17, 16, 15, 8, 22, 21, 20, 19, 12, 25, 24, 7, 170, 29, 28, 27, 16, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 21, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 23, 505, 81, 80, 79, 78, 77, 76, 75, 74, 73

Offset: 3

Author

Bob Selcoe, Apr 01 2015

Keywords

• nonn

Comments

Let A166133 = B; A166133 is defined as: After b(1)=1, b(2)=2, and b(3)=4, b(n+1) is the smallest divisor of b(n)^2-1 that has not yet appeared in the sequence.

A256557(n) = A166133(n)^2-1. Therefore, a(n) = (A166133(n)^2-1)/A166133(n+1), n>=3; that is, a(n) is A256557(n) divided by the smallest divisor of A166133(n+1)^2-1 which has not yet appeared in A166133. For example, a(12) = 5 means that 5 is A256557(12) = A166133(12)^2-1 = 80 divided its smallest divisor which has not yet appeared in A166133 (i.e., 16).

Examples

			a(13) = 17 because A256557(13)/A166133(14) = 255/15 = 17.
		

Crossrefs

Cf. A166133, A256557.

Programs

Mathematica

lim = 200; s = {1, 2, 4}; Do[d = Divisors[Last[s]^2 - 1]; i = 1; While[i <= Length[d] && MemberQ[s, d[[i]]], i++]; s = Append[s, d[[i]]], {lim}]; a166133 = Table[s[[k]], {k, 1, lim}]; a256557 = #^2 - 1 & /@ a166133; t = PadLeft[Most@a256557, lim]; Drop[t/a166133, 3] (* Michael De Vlieger, Apr 02 2015, after Hans Havermann at A166133 *)