A192584 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, 8, and 10 are in S.

2, 4, 5, 6, 8, 10, 11, 13, 17, 23, 31, 37, 41, 47, 53, 61, 67, 79, 83, 89, 101, 103, 107, 131, 137, 139, 149, 167, 179, 223, 263, 269, 283, 311, 317, 359, 367, 499, 557, 607, 619, 643, 719, 787, 809, 823, 857, 1031, 1049, 1097, 1193, 1433, 1439, 1579, 1619

Offset: 1

Author

Clark Kimberling, Jul 04 2011

Keywords

• nonn
• fini
• full

Comments

See the discussions at A192580 and A192584. The number of terms in this finite sequence is 104. The greatest term is 15845273.

Links

• Giovanni Resta, Table of n, a(n) for n = 1..104 (full sequence)

Crossrefs

Cf. A192476, A192580, A192583.

Programs

Mathematica

start = {2, 4, 6, 8, 10}; 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 *)

Extensions

Corrected by Giovanni Resta, Mar 21 2013