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%I #7 Jul 23 2021 09:03:58
%S 0,0,1,1,1,1,2,2,0,2,3,1,3,1,1,3,1,2,3,3,1,2,3,1,4,2,1,5,1,1,5,3,1,2,
%T 4,1,3,4,2,5,3,1,4,2,2,6,2,1,3,2,3,5,4,1,5,5,1,6,3,2,5,1,2,2,4,3,5,4,
%U 0,7,4,1,6,3,1,5,2,2,5,6,1,2,5,2,7,4,2,6,2,2,9,2,3,4,4,2,2,4,1,9,5,3,5,5,3
%N Number of ways to express 2n-1 as p+2a^2; p prime, a > 0.
%C Similar to A046921 and A046923. Sequence A060003 lists the odd numbers having no representations.
%H T. D. Noe, <a href="/A143539/b143539.txt">Table of n, a(n) for n=1..10000</a>
%H L. Hodges, <a href="https://www.jstor.org/stable/2690477">A lesser-known Goldbach conjecture</a>, Math. Mag., 66 (1993), 45-47.
%e a(11)=3 because 21 = 19+2*1^2 = 13+2*2^2 = 3+2*3^2.
%t Table[cnt=0; Do[If[PrimeQ[n-2*k^2], cnt++ ], {k,Floor[Sqrt[n/2]]}]; cnt, {n,1,20000,2}]
%K nonn
%O 1,7
%A _T. D. Noe_, Aug 23 2008
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