A128687 Smallest odd nonprime such that every subset of a(1), ..., a(n) adds to a nonprime.

1, 9, 15, 39, 105, 731, 2805, 59535, 2658795, 78060135, 67554224745

Offset: 1

Author

T. D. Noe, Mar 20 2007

Keywords

• hard
• nonn

Comments

The first 8 terms are from Rivera's puzzle 84.

The sequences is infinite [Chris Nash]. - N. J. A. Sloane, Jan 20 2017

Links

• Chris Nash, Proof that A052349, A128687, and A128688 are infinite [Cached copy of proof, from The Prime Puzzles and Problems website]
• Carlos Rivera, Puzzle 84. Non-primes adding up to non-primes, The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A052349 (no restrictions on even or odd), A128688 (restricted to even numbers).

Programs

Mathematica

a[1]=1; a[n_]:=a[n]=(s=Subsets[Array[a,n-1],n-1]; c=a[n-1]; While[d=1;While[!PrimeQ[Total[s[[d]]]+c]&&dGiorgos Kalogeropoulos, Nov 19 2021 *)

Extensions

a(11) from Donovan Johnson, Apr 18 2010