OFFSET
1,2
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.
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.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Bob Selcoe, Apr 01 2015
STATUS
approved