A359443 Primes p such that if q is the next prime, the sum (with multiplicity) of prime factors of p^2 + q^2 is a square.

11, 17, 23, 79, 131, 229, 1019, 1123, 1583, 3299, 4019, 4091, 15307, 28813, 29147, 35083, 35933, 43427, 43597, 47809, 68683, 69029, 72047, 80173, 80513, 82483, 83257, 84263, 92567, 94583, 100693, 118603, 129517, 155317, 163243, 165553, 190181, 191021, 198901, 199211, 223439, 225721, 257273, 265117

Offset: 1

Author

Robert Israel, Jan 01 2023

Keywords

• nonn

Comments

Suggested in an email by J. M. Bergot.

Primes prime(k) such that prime(k)^2 + prime(k+1)^2 is in A051448.

Examples

			a(3) = 23 is a term because 23 and 29 are consecutive primes with 23^2 + 29^2 = 1370 = 2*5*137, and 2+5+137 = 144 = 12^2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A001414, A051448.

Programs

Maple

q:= 2: R:= NULL: count:=0:
while count < 100 do
  p:= q; q:= nextprime(p);
  s:= p^2 + q^2;
  if issqr(add(t[1]*t[2], t = ifactors(s)[2])) then
    R:= R, p; count:= count+1;
  fi;
od:
R;