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A347163 Primes p such that 10*p can be written as a^2+b^2 where a and b are prime. 1
5, 13, 17, 29, 37, 41, 53, 89, 97, 101, 113, 137, 149, 173, 197, 233, 257, 269, 281, 293, 317, 349, 353, 373, 389, 401, 449, 461, 509, 521, 557, 569, 593, 617, 641, 653, 677, 701, 761, 773, 797, 809, 821, 857, 881, 929, 953, 977, 1013, 1021, 1049, 1061, 1097, 1109, 1181, 1193, 1217, 1229, 1289 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Pythagorean primes p = x^2+y^2 where 3*x+y and |x-3*y| or x+3*y and |3*x-y| are primes.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

a(3) = 17 is a term because 170 = 7^2+11^2 with 17, 7 and 11 all prime.

MAPLE

filter:= proc(p) local F, a, b; uses GaussInt;

  if not isprime(p) then return false fi;

  F:= GIfactors(p)[2][1][1];

  a:= abs(Re(F)); b:= abs(Im(F));

  (isprime(a+3*b) and isprime(abs(3*a-b))) or (isprime(3*a+b) and isprime(abs(3*b-a)))

end proc:

select(filter, [seq(i, i=5..10000, 4)]);

MATHEMATICA

Select[Prime@Range@300, Select[PowersRepresentations[10#, 2, 2], And@@PrimeQ@#&]!={}&] (* Giorgos Kalogeropoulos, Aug 20 2021 *)

CROSSREFS

Contained in A002144.

Sequence in context: A319287 A192592 A349900 * A111055 A307096 A283391

Adjacent sequences:  A347160 A347161 A347162 * A347164 A347165 A347166

KEYWORD

nonn

AUTHOR

J. M. Bergot and Robert Israel, Aug 20 2021

STATUS

approved

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Last modified August 14 10:20 EDT 2022. Contains 356114 sequences. (Running on oeis4.)