cp's OEIS Frontend

A144590 Number of ordered ways of writing 2n+1 = i + j, where i is a prime and j is of the form k*(k+1), k > 0.

%I A144590 #18 May 23 2024 04:25:30
%S A144590 0,0,1,1,2,1,2,2,2,3,1,3,4,1,2,3,3,3,3,2,2,5,2,3,6,1,4,3,1,5,5,3,3,4,
%T A144590 2,3,7,3,3,6,2,4,6,2,4,5,3,5,3,3,5,8,1,2,9,1,7,7,3,5,5,3,3,5,4,4,7,2,
%U A144590 4,8,2,7,5,2,4,8,3,4,6,4,6,7,2,2,12,2,6,5,2,8,5,4,6,7,2,4,11,3,4,10,3,7,6,2
%N A144590 Number of ordered ways of writing 2n+1 = i + j, where i is a prime and j is of the form k*(k+1), k > 0.
%C A144590 Based on a posting by _Zhi-Wei Sun_ to the Number Theory Mailing List, Mar 23 2008, where he conjectures that a(n) > 0 for n >= 2.
%C A144590 _Zhi-Wei Sun_ has offered a monetary reward for settling this conjecture.
%C A144590 No counterexample exists below 10^10 (_D. S. McNeil_).
%D A144590 Zhi-Wei Sun, On sums of primes and triangular numbers, Journal of Combinatorics and Number Theory, 1(2009), no.1, 65-76.
%H A144590 T. D. Noe, <a href="/A144590/b144590.txt">Table of n, a(n) for n = 0..10000</a>
%H A144590 Zhi-Wei Sun, <a href="http://listserv.nodak.edu/cgi-bin/wa.exe?A1=ind0803&amp;L=nmbrthry">Posing to Number Theory List (1)</a>
%H A144590 Zhi-Wei Sun, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;9ebd2e77.0803">Posting to Number Theory List (2)</a>
%H A144590 Zhi-Wei Sun, <a href="https://arxiv.org/abs/0803.3737">On sums of primes and triangular numbers</a>, arXiv:0803.3737 [math.NT], 2008-2009.
%Y A144590 Cf. A132399. Bisection of A117054.
%K A144590 nonn,easy
%O A144590 0,5
%A A144590 _N. J. A. Sloane_, Jan 15 2009