A124044 Number of ways to express 4n+3 as the sum of an odd square and twice a prime.

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, 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, 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

Offset

0,4

Comments

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

No others below 10^9. Heuristics suggest there are no more. - Charles R Greathouse IV, Sep 13 2013

References

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

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

Links

T. D. Noe, Table of n, a(n) for n = 0..10000

Example

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

Maple

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);

Crossrefs

Sequence in context: A217581 A366521 A348581 * A059981 A033676 A095165

Adjacent sequences: A124041 A124042 A124043 * A124045 A124046 A124047

Keyword

easy,nonn

Author

Robert Israel, Nov 02 2006

Status

approved