%I #18 Jul 22 2021 09:18:25

%S 1,2,2,2,2,2,3,2,1,4,3,2,3,1,2,4,2,2,4,3,2,3,3,2,4,3,2,5,1,2,6,3,1,3,

%T 4,2,5,4,2,6,3,2,4,2,3,6,2,1,4,3,4,6,4,2,6,5,2,6,3,2,5,1,2,3,5,4,5,4,

%U 1,8,4,1,6,3,2,6,2,2,6,6,1,4,5,3,7,4,3,6,2,3,10,2,3,4,4,3,3,4,2

%N Number of ways to express 2n+1 as p+2a^2; p = 1 or prime, a >= 0.

%C Goldbach conjectured this sequence is never zero.

%C The only zero terms appear to be for the odd numbers 5777 and 5993. - _T. D. Noe_, Aug 23 2008

%H T. D. Noe, <a href="/A046921/b046921.txt">Table of n, a(n) for n = 0..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.

%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>

%F a(n) = A046920(A005408(n)). - _Reinhard Zumkeller_, Apr 03 2013

%o (Haskell)

%o a046921 = a046920 . a005408 -- _Reinhard Zumkeller_, Apr 03 2013

%Y Cf. A042978, A046920, A046922, A046923, A060003, A143539.

%Y Cf. A007697.

%K nonn

%O 0,2

%A _David W. Wilson_