A192585 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, 5, 8, 11, and 14 are in S.

2, 5, 8, 11, 14, 17, 23, 29, 41, 47, 59, 71, 83, 89, 113, 137, 167, 179, 197, 227, 233, 239, 359, 467, 479, 569, 659, 719, 827, 1097, 1163, 1319, 1433, 1439, 1583, 1913, 2339, 2879, 3167, 3347, 3833, 4679, 5273, 9227, 10067, 11579, 15359, 18713, 20063

Offset: 1

Author

Clark Kimberling, Jul 05 2011

Keywords

• nonn
• fini
• full

Comments

Last term is a(70) = 15785183. - Giovanni Resta, Mar 21 2013

Links

• Giovanni Resta, Table of n, a(n) for n = 1..70 (full sequence)

Crossrefs

Cf. A192476, A192580, A192584.

Programs

Mathematica

start = {2, 5, 8, 11, 14}; 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 *)