A192588 Monotonic ordering of set S generated by these rules: if x and y are in S and xy-1 is a prime, then xy-1 is in S, and 2, 4, 6, and 8 are in S.

2, 3, 4, 5, 6, 7, 8, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 61, 67, 73, 101, 103, 113, 137, 151, 163, 173, 257, 281, 401, 487, 547, 617, 677, 691, 821, 823, 977, 1093, 1123, 1303, 1381, 2467, 2707, 3701, 3907, 4933, 4937, 5413, 5527, 5861, 6737, 7817

Offset: 1

Author

Clark Kimberling, Jul 05 2011

Keywords

• nonn
• fini
• full

Comments

See the discussions at A192476 and A192580.

Last term is a(61) = 62533. - Giovanni Resta, Mar 21 2013

Links

• Giovanni Resta, Table of n, a(n) for n = 1..61 (full sequence)

Crossrefs

Cf. A192476, A192580, A192586, A192587.

Programs

Mathematica

start = {2, 4, 6, 8}; seq = {}; new = start; While[new != {}, seq = Union[seq, new]; fresh = new; new = {}; Do[If[PrimeQ[u = x*y - 1], If[! MemberQ[seq, u], AppendTo[new, u]]], {x, seq}, {y, fresh}]]; seq (* Giovanni Resta, Mar 21 2013 *)