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A100570 Positive integers that cannot be partitioned into the sum of a semiprime and a square. Squares include 0 and 1. 8

%I

%S 1,2,3,12,17,28,32,72,108,117,297,657

%N Positive integers that cannot be partitioned into the sum of a semiprime and a square. Squares include 0 and 1.

%C No others up to 300000. Computed in collaboration with _Ray Chandler_. It appears that this sequence is finite, that is, that almost every positive integer is the sum of a semiprime and a square number. There are probably no further exceptions after a(12)=657.

%C The statement about the finiteness of this sequence (namely, a(n)<=657) is much stronger than the Goldbach binary conjecture. Indeed, a much weaker conjecture, that this sequence contains no perfect squares >1, already implies the Goldbach conjecture. Cf. comment in A241922. - _Vladimir Shevelev_, May 01 2014

%F a(n) is not an element for any integers i, j of the pairwise sum of {A001358(i)} and {A000290(j)}.

%Y Cf. A000290, A001358, A046903.

%K easy,nonn,more

%O 1,2

%A _Jonathan Vos Post_, Nov 29 2004

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Last modified March 25 22:28 EDT 2019. Contains 321477 sequences. (Running on oeis4.)