login
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.
1
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
1,1
COMMENTS
Suggested in an email by J. M. Bergot.
Primes prime(k) such that prime(k)^2 + prime(k+1)^2 is in A051448.
LINKS
EXAMPLE
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.
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;
CROSSREFS
Sequence in context: A261918 A136342 A126609 * A079367 A120139 A191061
KEYWORD
nonn
AUTHOR
Robert Israel, Jan 01 2023
STATUS
approved