A359492 a(n) is the least number of the form p^2 + q^2 - 2 for primes p and q that is an odd prime times 2^n, or -1 if there is no such number.

11, 6, -1, 56, 48, 96, 192, 384, 2816, 1536, 109568, 10582016, 12288, 7429922816, 64176128, 4318724096, 196608, 60486975488, 9388028592128, 849566088298496, 214058289594368, 896029329195008

Offset: 0

Author

Robert Israel, Jan 02 2023

Keywords

• sign
• more

Comments

If a(n) > -1 then a(n) >= A359439(n).

a(22) <= 10228945815339008; a(23) <= 188039754665689088; a(24) <= 54409680373415936; a(25) <= 246561971023904768; a(26) <= 966464636658384896. - Daniel Suteu, Jan 05 2023

Examples

			a(4) = 48 = 3*2^4 = 5^2 + 5^2 - 2.
		

Crossrefs

Cf. A045636, A359439.

Programs

Maple

f:= proc(n) local b,t,s,x,y;
    t:= 2^n; b:= 2;
    do
      b:= nextprime(b);
      if member(3, numtheory:-factorset(b*t+2) mod 4) then next fi;
      if ormap(s -> 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..18]);

Extensions

a(19)-a(21) from Daniel Suteu, Jan 05 2023