A208882 Number of representations of square of prime(n) as a^2 + b^2 + c^2 with 0 < a <= b <= c.

0, 1, 0, 1, 2, 1, 2, 3, 3, 3, 4, 4, 5, 6, 6, 6, 8, 7, 9, 9, 9, 10, 11, 11, 12, 12, 13, 14, 13, 14, 16, 17, 17, 18, 18, 19, 19, 21, 21, 21, 23, 22, 24, 24, 24, 25, 27, 28, 29, 28, 29, 30, 30, 32, 32, 33, 33, 34, 34, 35, 36, 36, 39, 39, 39, 39, 42, 42, 44, 43, 44

Offset

1,5

Comments

Almost monotonically increasing sequence, only rarely a(n) <= a(n-1), contrary to case of n instead of prime(n) (A181786).

Links

Samuel Harkness, Table of n, a(n) for n = 1..1229

Example

a(2)=1 because prime(2)=3 and 3^2 = 1^2 + 2^2 + 2^2,
a(4)=1 because prime(4)=7 and 7^2 = 2^2 + 3^2 + 6^2,
a(5)=2 because prime(5)=11 and 11^2 = 2^2 + 6^2 + 9^2 = 6^2 + 6^2 + 7^2.

Mathematica

Table[Length[FindInstance[{Prime[n]^2==a^2+b^2+c^2, 0<a<=b<=c}, {a, b, c}, Integers, 100]], {n, 80}] (* Harvey P. Dale, Mar 06 2020 *)

Crossrefs

Cf. A002144, A181786.

Sequence in context: A228285 A020908 A240873 * A186519 A241091 A137719

Adjacent sequences: A208879 A208880 A208881 * A208883 A208884 A208885

Keyword

nonn

Author

Zak Seidov, Mar 02 2012

Status

approved