OFFSET
0,1
COMMENTS
Suggested by an email from J. M. Bergot.
a(2) = -1 because if p and q are odd primes, p^2 + q^2 - 2 is divisible by 8.
EXAMPLE
a(0) = 11 = 2^2 + 3^2 - 2 = 11*2^0.
a(1) = 6 = 2^2 + 2^2 - 2 = 3*2^1.
a(3) = 56 = 3^2 + 7^2 - 2 = 7*2^3.
a(4) = 16 = 3^2 + 3^2 - 2 = 1*2^4.
MAPLE
f:= proc(n) local b, t, s, x, y;
t:= 2^n;
for b from 1 by 2 do
if ormap(s -> subs(s, x) <= subs(s, y) and isprime(subs(s, x)) and isprime(subs(s, y)), [isolve(x^2+y^2-2=b*t)]) then return b*t fi
od;
end proc:
f(2):= -1:
map(f, [$0..40]);
CROSSREFS
KEYWORD
sign
AUTHOR
Robert Israel, Jan 02 2023
STATUS
approved