

A052349


Lexicographically earliest sequence of distinct positive integers such that no subsequence sums to a prime.


13



1, 8, 24, 25, 86, 1260, 1890, 14136, 197400, 10467660, 1231572090, 682616834970
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OFFSET

1,2


COMMENTS

This set was defined by T. W. A. Baumann in The Prime Puzzles and Problems pages. He and C. Rivera obtained the first 10 members. Chris Nash proved that this sequence is infinite.


LINKS

Table of n, a(n) for n=1..12.
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


EXAMPLE

a(4) = 25 as 25+1, 25+8, 25+24, 25+1+8, 25+1+24, 25+8+24 and finally 25+1+8+24 all are composite numbers.


CROSSREFS

Cf. A068638.
Cf. A128687 (restricted to odd numbers), A128688 (restricted to even numbers).
Sequence in context: A128637 A280708 A109272 * A254448 A029607 A244030
Adjacent sequences: A052346 A052347 A052348 * A052350 A052351 A052352


KEYWORD

hard,more,nonn,nice


AUTHOR

Carlos Rivera, Mar 07 2000


EXTENSIONS

One more term from T. D. Noe, Mar 20 2007
a(12) from Donovan Johnson, Jun 26 2010
New name from Charles R Greathouse IV, Jan 13 2014
Name clarified by Peter Kagey, Jan 07 2017


STATUS

approved



