cp's OEIS Frontend

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.

%I A359492 #17 Jan 06 2023 10:43:50
%S A359492 11,6,-1,56,48,96,192,384,2816,1536,109568,10582016,12288,7429922816,
%T A359492 64176128,4318724096,196608,60486975488,9388028592128,849566088298496,
%U A359492 214058289594368,896029329195008
%N 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.
%C A359492 If a(n) > -1 then a(n) >= A359439(n).
%C A359492 a(22) <= 10228945815339008; a(23) <= 188039754665689088; a(24) <= 54409680373415936; a(25) <= 246561971023904768; a(26) <= 966464636658384896. - _Daniel Suteu_, Jan 05 2023
%e A359492 a(4) = 48 = 3*2^4 = 5^2 + 5^2 - 2.
%p A359492 f:= proc(n) local b,t,s,x,y;
%p A359492     t:= 2^n; b:= 2;
%p A359492     do
%p A359492       b:= nextprime(b);
%p A359492       if member(3, numtheory:-factorset(b*t+2) mod 4) then next fi;
%p A359492       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
%p A359492     od;
%p A359492 end proc:
%p A359492 f(2):= -1:
%p A359492 map(f, [$0..18]);
%Y A359492 Cf. A045636, A359439.
%K A359492 sign,more
%O A359492 0,1
%A A359492 _Robert Israel_, Jan 02 2023
%E A359492 a(19)-a(21) from _Daniel Suteu_, Jan 05 2023