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%I #33 Apr 26 2015 10:06:19
%S 1,2,5,11,23,43,47,137,157,293,439,1163,1201,2339,3529,5867,9391,
%T 23623,24659,49477,72953,147083,195511,392059,538001,1052479,1590467,
%U 2520503,4503007,5041007,14047027,15637483,28239989,55404001,115994933,210773399
%N Lexicographically least sequence of primes (including 1) that are sum-free.
%C 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.
%H Giovanni Resta, <a href="/A225947/b225947.txt">Table of n, a(n) for n = 1..40</a>
%H H. L. Abbott, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa48/aa4819.pdf">On sum-free sequences</a>, Acta Arithmetica, 1987, Vol 48, Issue 1, pp. 93-96.
%H C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_127.htm">Prime Puzzle 127</a>
%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/A-Sequence.html">A-Sequence</a> (MathWorld)
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Sum-free_sequence">Sum-free sequence</a>
%e 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).
%t 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
%Y Cf. A060341, A064934, A075058.
%K nonn
%O 1,2
%A _Frank M Jackson_, May 21 2013
%E a(23) - a(32) from _Zak Seidov_, May 23 2013
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