A225947 Lexicographically least sequence of primes (including 1) that are sum-free.

1, 2, 5, 11, 23, 43, 47, 137, 157, 293, 439, 1163, 1201, 2339, 3529, 5867, 9391, 23623, 24659, 49477, 72953, 147083, 195511, 392059, 538001, 1052479, 1590467, 2520503, 4503007, 5041007, 14047027, 15637483, 28239989, 55404001, 115994933, 210773399

Offset: 1

Author

Frank M Jackson, May 21 2013

Keywords

• nonn

Comments

A sum-free sequence has no term that is the sum of a subset of its previous terms. There are an infinite number of sequences that are subsets of {1} union primes and sum-free. This sequence is lexicographically the first.

Examples

			a(8)=137 as 137 is the next prime after a(7)=47 that cannot be formed from distinct sums of a(1),...,a(7) (1,2,5,11,23,43,47).
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..40
• H. L. Abbott, On sum-free sequences, Acta Arithmetica, 1987, Vol 48, Issue 1, pp. 93-96.
• Carlos Rivera, Puzzle 127. Non adding prime sequences, The Prime Puzzles & Problems Connection.
• Eric Weisstein's World of Mathematics, A-Sequence
• Wikipedia, Sum-free sequence

Crossrefs

Cf. A060341, A064934, A075058.

Programs

Mathematica

memberQ[n1_, k1_] := If[Select[IntegerPartitions[Prime[n1], Length[k1], k1], Sort@#==Union@# &]=={}, False, True]; k={1}; n=1; While[Length[k]<15, (If[!memberQ[n, k], k=Append[k, Prime[n]]]; n++)]; k

Extensions

a(23)-a(32) from Zak Seidov, May 23 2013