A123592 Primes of the form p^2 + q^2 + r^2, where p,q,r are primes.

17, 43, 59, 67, 83, 107, 139, 179, 227, 251, 307, 347, 379, 419, 467, 491, 547, 563, 587, 659, 827, 859, 971, 1019, 1091, 1259, 1427, 1499, 1667, 1699, 1811, 1867, 1907, 1931, 1979, 2027, 2243, 2267, 2339, 2531, 2579, 2699, 2819, 2843, 2939, 3347, 3371, 3499

Offset

1,1

Comments

a(n) is a subset of A085317(n) = {3, 11, 17, 19, 29, 41, 43, 53, 59, 61, 67, 73, 83, ...} Primes of form x^2 + y^2 + z^2. All terms except a(1) = 17 are congruent to 3 mod 8.

If neither p, q, nor r is 3, then p^2 + q^2 + r^2 is always divisible by 3. Therefore all terms in a(n) have at least one 3^2 in their summation. - Richard R. Forberg, Aug 29 2013

Links

Table of n, a(n) for n=1..48.

Example

a(1) = 17 because 17 = 2^2 + 2^2 + 3^2 is prime and 2^2 + 2^2 + 2^2 = 12 is composite.

Mathematica

With[{nn=50}, Take[Union[Select[Total/@Tuples[Prime[Range[nn/2]]^2, 3], PrimeQ]], nn]] (* Harvey P. Dale, Aug 26 2015 *)

Crossrefs

Cf. A085317 (primes of form x^2 + y^2 + z^2).

Sequence in context: A195685 A118587 A215164 * A260553 A165285 A200321

Adjacent sequences: A123589 A123590 A123591 * A123593 A123594 A123595

Keyword

nonn

Author

Alexander Adamchuk, Nov 14 2006

Status

approved