A045698 Number of ways n can be written as the sum of two squares of primes.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0

Offset

0,339

Comments

a(A214879(n)) = 0; a(A045636(n)) > 0; a(A214723(n)) = 1; a(A214511(n)) = n and a(m) < n for m < A214511(n). - Reinhard Zumkeller, Jul 29 2012

The smallest value of n such that a(n) = 2 is 338. (This helps distinguish it from the characteristic function of A045636.) - Wesley Ivan Hurt, Jun 13 2013

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for sequences related to sums of squares

Example

For example, a(29) = 1 because 29 = 2^2 + 5^2. a(3) = 0 because there is no way to write 3 as sum of two squares of primes.

Prog

(Haskell)
a045698 n = length $ filter (\x -> x > 0 && a010051' x == 1) $
map (a037213 . (n -)) $
takeWhile (<= div n 2) a001248_list
-- Reinhard Zumkeller, Jul 29 2012
(PARI) a(n)=my(s=0, q); forprime(p=2, sqrtint(n\2), if(issquare(n-p^2, &q)&&isprime(q), s++)); s \\ Charles R Greathouse IV, Jun 04 2014

Crossrefs

Cf. A001248, A010051, A037213.

Sequence in context: A169674 A324053 A353480 * A106197 A369048 A011722

Adjacent sequences: A045695 A045696 A045697 * A045699 A045700 A045701

Keyword

easy,nonn

Author

Felice Russo

Extensions

More terms from Erich Friedman

Status

approved