A282971 Number of compositions (ordered partitions) of n into primes of form x^2 + y^2 (A002313).

1, 0, 1, 0, 1, 1, 1, 2, 1, 3, 2, 4, 4, 6, 7, 9, 11, 15, 18, 24, 29, 37, 48, 58, 78, 92, 124, 149, 195, 243, 308, 393, 490, 629, 786, 1004, 1263, 1603, 2024, 2564, 3239, 4106, 5184, 6571, 8301, 10508, 13298, 16807, 21296, 26895, 34082, 43060, 54528, 68952, 87245, 110392, 139622, 176696, 223484, 282798, 357731

Offset: 0

Author

Ilya Gutkovskiy, Feb 25 2017

Keywords

• nonn

Comments

Number of compositions (ordered partitions) of n into primes congruent to 1 or 2 mod 4.

Conjecture: every number > 16 is the sum of at most 4 primes of form x^2 + y^2.

Examples

			a(12) = 4 because we have [5, 5, 2], [5, 2, 5], [2, 2, 5] and [2, 2, 2, 2, 2, 2].
		

Links

• Index entries for sequences related to compositions

Crossrefs

Cf. A002124, A002313, A023360, A077608, A280917, A282906, A282970.

Programs

Mathematica

nmax = 60; CoefficientList[Series[1/(1 - Sum[Boole[SquaresR[2, k] != 0 && PrimeQ[k]] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

PARI

Vec(1/(1 - sum(k=1, 60, (isprime(k) && k%4<3)*x^k)) + O(x^61)) \\ Indranil Ghosh, Mar 15 2017

Formula

G.f.: 1/(1 - Sum_{k>=1} x^A002313(k)).