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A128687 Smallest odd nonprime such that every subset of a(1), ..., a(n) adds to a nonprime. 3
1, 9, 15, 39, 105, 731, 2805, 59535, 2658795, 78060135, 67554224745 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

Table of n, a(n) for n=1..11.

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]; While[d=1; While[!PrimeQ[Total[s[[d]]]+c]&&d<Length@s, d++]; d!=Length@s||PrimeQ[Total[s[[d]]]+c]||PrimeQ@c, c=c+2]; c); Array[a, 8] (* Giorgos Kalogeropoulos, Nov 19 2021 *)

CROSSREFS

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

Sequence in context: A307217 A100556 A057478 * A193579 A274757 A146789

Adjacent sequences:  A128684 A128685 A128686 * A128688 A128689 A128690

KEYWORD

hard,nonn,changed

AUTHOR

T. D. Noe, Mar 20 2007

EXTENSIONS

a(11) from Donovan Johnson, Apr 18 2010

STATUS

approved

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Last modified December 4 09:43 EST 2021. Contains 349485 sequences. (Running on oeis4.)