A225947 - OEIS

%I #37 Feb 16 2025 08:33:19

%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 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_127.htm">Puzzle 127. Non adding prime sequences</a>, The Prime Puzzles & Problems Connection.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/A-Sequence.html">A-Sequence</a>

%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