

A123592


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


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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



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).


KEYWORD

nonn


AUTHOR



STATUS

approved



