A124044 - OEIS

%I #11 Aug 06 2019 02:41:46

%S 0,1,1,2,1,2,1,2,3,2,1,3,1,2,3,3,1,3,2,0,4,4,2,4,1,2,4,2,2,3,2,3,4,3,

%T 1,6,3,1,4,3,1,6,2,3,3,4,2,3,4,1,6,4,1,6,2,2,7,3,2,4,4,2,4,4,2,6,2,2,

%U 4,3,3,6,1,2,6,5,3,5,4,1,5,6,1,6,2,3,6,3,2,4,4,3,6,5,1,9,4,2,8,3,2

%N Number of ways to express 4n+3 as the sum of an odd square and twice a prime.

%C Is there any n > 19 for which a(n) = 0? There are no others below 50000.

%C No others below 10^9. Heuristics suggest there are no more. - _Charles R Greathouse IV_, Sep 13 2013

%D Underwood Dudley, "Mathematical Cranks", Mathematical Association of America 1992, p. 240.

%D Sci.math thread "Conjecture in 'Mathematical Cranks'", November 2006.

%H T. D. Noe, <a href="/A124044/b124044.txt">Table of n, a(n) for n = 0..10000</a>

%e 4*3 + 3 = 15 = 1^2 + 2*7 = 3^2 + 2*3, so a(3) = 2.

%p f:= n -> nops(select(isprime,[seq]((4*n+3-(2*i+1)^2)/2,i=0..floor((sqrt(4*n+3)-1)/2)))): [seq](f(n),n=0..100);

%K easy,nonn

%O 0,4

%A _Robert Israel_, Nov 02 2006