A128688 a(1)=1. For n>1, a(n) is the smallest even number such that every subset of a(1), ..., a(n) adds to a nonprime.

1, 8, 24, 86, 90, 780, 5940, 52350, 278460, 40768260, 6847205430, 5027286840810

Offset

1,2

Comments

The first 7 terms are from Rivera's puzzle 84.

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

Links

Table of n, a(n) for n=1..12.

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.

Mathematica

a[1] = 1; a[n_] := a[n] = (s = Subsets[Array[a, n-1], n-1]; c = a[n-1] + 1; While[d = 1; While[!PrimeQ[Total[s[[d]]] + c] && d < Length@s, d++]; d != Length@s || PrimeQ[Total[s[[d]]] + c] || OddQ@c, c++]; c); Array[a, 8] (* Giorgos Kalogeropoulos, Nov 19 2021 *)

Crossrefs

Cf. A052349 (no restrictions on even or odd), A128687 (restricted to odd numbers).

Sequence in context: A296400 A297808 A097544 * A279162 A217016 A019260

Adjacent sequences: A128685 A128686 A128687 * A128689 A128690 A128691

Keyword

hard,nonn

Author

T. D. Noe, Mar 20 2007

Extensions

a(11) from Donovan Johnson, Apr 18 2010

a(12) from Donovan Johnson, Jul 06 2010

Status

approved