A033210 -id:A033210 - cp's OEIS frontend

A248215 Primes of form x^2+13*y^2 (mod 52).

13, 17, 29, 1, 9, 49, 9, 1, 17, 25, 25, 49, 9, 17, 1, 25, 9, 25, 17, 1, 49, 29, 17, 29, 49, 1, 25, 29, 17, 29, 49, 25, 49, 1, 17, 9, 25, 9, 29, 1, 17, 25, 9, 49, 17, 1, 29, 49, 1, 9, 29, 25, 29, 49, 25, 49, 1, 9, 25, 29, 17, 25, 9, 1, 17, 29, 9, 25, 49, 17, 1, 25, 1, 9, 49, 9, 29, 29, 1, 9, 1, 17

Offset: 1

Zak Seidov, Oct 04 2014

nonn

Primes of form x^2+13*y^2 are congruent to {1, 9, 13, 17, 25, 29, or 49} (mod 52). Among first 10000 such primes (A033210), the corresponding frequences are: 1664, 1665, 1, 1667, 1661, 1666, 1676 - remarkably uniform distribution except for prime 13.

Cf. A033210.

A248408 Values of y in A142508(n) = x^2+13y^2.

Original entry on oeis.org

2, 1, 3, 5, 2, 4, 6, 9, 10, 1, 12, 10, 7, 7, 13, 13, 14, 2, 15, 16, 8, 13, 16, 5, 7, 19, 7, 11, 2, 6, 4, 13, 6, 8, 22, 21, 10, 21, 24, 10, 17, 20, 25, 3, 7, 22, 19, 16, 26, 21, 11, 18, 28, 18, 23, 26, 30, 10, 29, 31, 31, 28, 32, 24, 1, 24, 5, 21, 5, 7, 26, 18, 29, 11, 33, 20, 32, 35, 15, 28, 2, 22

Offset: 1

Zak Seidov, Oct 06 2014

nonn

			a(1)=2 because A142508(1)=53=1^2+13*2^2 (x=1,y=2);
a(2)=1 because A142508(2)=157=12^2+13*1^2 (x=12, y=1).

Cf. A033210, A142508, A248221, A248019(values of x).

cp's OEIS Frontend

A248215 Primes of form x^2+13*y^2 (mod 52).

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A248408 Values of y in A142508(n) = x^2+13y^2.

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