A128688 - OEIS

%I #22 Nov 21 2021 07:38:19

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

%N 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.

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

%C The sequences is infinite [Chris Nash]. - _N. J. A. Sloane_, Jan 20 2017

%H Chris Nash, <a href="/A052349/a052349.txt">Proof that A052349, A128687, and A128688 are infinite</a> [Cached copy of proof, from The Prime Puzzles and Problems website]

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_084.htm">Puzzle 84. Non-primes adding up to non-primes</a>, The Prime Puzzles and Problems Connection.

%t 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 *)

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

%K hard,nonn

%O 1,2

%A _T. D. Noe_, Mar 20 2007

%E a(11) from _Donovan Johnson_, Apr 18 2010

%E a(12) from _Donovan Johnson_, Jul 06 2010