A256557 a(n) = A166133(n)^2 - 1.

0, 3, 15, 8, 63, 48, 35, 24, 143, 120, 99, 80, 255, 224, 195, 168, 440, 399, 360, 323, 288, 575, 528, 483, 4760, 783, 728, 675, 624, 1520, 1443, 1368, 1295, 1224, 1155, 1088, 1023, 960, 899, 840, 1599, 1680, 1763, 1848, 1935, 2024, 2115, 2208

Offset: 1

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.

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

Crossrefs

Cf. A166133, A256559.

Programs

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 *)

Formula

a(n) = A166133(n+1)*A256559(n)