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 A123592 Primes of the form p^2 + q^2 + r^2, where p,q,r are primes. 1

%I #14 Aug 26 2015 12:46:19

%S 17,43,59,67,83,107,139,179,227,251,307,347,379,419,467,491,547,563,

%T 587,659,827,859,971,1019,1091,1259,1427,1499,1667,1699,1811,1867,

%U 1907,1931,1979,2027,2243,2267,2339,2531,2579,2699,2819,2843,2939,3347,3371,3499

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

%C 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.

%C 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

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

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

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

%K nonn

%O 1,1

%A _Alexander Adamchuk_, Nov 14 2006

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Last modified September 7 22:13 EDT 2024. Contains 375749 sequences. (Running on oeis4.)