cp's OEIS Frontend

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.

%I A359443 #8 Jan 06 2023 03:24:41
%S A359443 11,17,23,79,131,229,1019,1123,1583,3299,4019,4091,15307,28813,29147,
%T A359443 35083,35933,43427,43597,47809,68683,69029,72047,80173,80513,82483,
%U A359443 83257,84263,92567,94583,100693,118603,129517,155317,163243,165553,190181,191021,198901,199211,223439,225721,257273,265117
%N 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.
%C A359443 Suggested in an email by _J. M. Bergot_.
%C A359443 Primes prime(k) such that prime(k)^2 + prime(k+1)^2 is in A051448.
%H A359443 Robert Israel, <a href="/A359443/b359443.txt">Table of n, a(n) for n = 1..2000</a>
%e A359443 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.
%p A359443 q:= 2: R:= NULL: count:=0:
%p A359443 while count < 100 do
%p A359443   p:= q; q:= nextprime(p);
%p A359443   s:= p^2 + q^2;
%p A359443   if issqr(add(t[1]*t[2], t = ifactors(s)[2])) then
%p A359443     R:= R, p; count:= count+1;
%p A359443   fi;
%p A359443 od:
%p A359443 R;
%Y A359443 Cf. A001414, A051448.
%K A359443 nonn
%O A359443 1,1
%A A359443 _Robert Israel_, Jan 01 2023