%I #14 Apr 02 2015 11:34:59
%S 0,3,15,8,63,48,35,24,143,120,99,80,255,224,195,168,440,399,360,323,
%T 288,575,528,483,4760,783,728,675,624,1520,1443,1368,1295,1224,1155,
%U 1088,1023,960,899,840,1599,1680,1763,1848,1935,2024,2115,2208
%N a(n) = A166133(n)^2 - 1.
%C 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.
%C Since it is conjectured that A166133 is a permutation of the natural numbers, it is therefore conjectured that this sequence is a permutation of all numbers of the form n^2-1.
%H Michael De Vlieger, <a href="/A256557/b256557.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A166133(n+1)*A256559(n)
%t 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]]], {5000}]; t = Table[s[[k]], {k, 1, 5000}]; #^2 - 1 & /@ t; (* _Michael De Vlieger_, Apr 02 2015, after _Hans Havermann_ at A166133 *)
%Y Cf. A166133, A256559.
%K nonn
%O 1,2
%A _Bob Selcoe_, Apr 01 2015