A359439 a(n) is the least number of the form p^2 + q^2 - 2 for primes p and q that is an odd multiple of 2^n, or -1 if there is no such number.

11, 6, -1, 56, 16, 32, 192, 128, 2816, 1536, 15360, 30720, 12288, 73728, 147456, 32768, 196608, 1179648, 22806528, 11010048, 34603008, 31457280, 314572800, 679477248, 50331648, 301989888, 1006632960, 10871635968, 20132659200, 4831838208, 28991029248, 173946175488, 450971566080, 77309411328

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.

Links

Table of n, a(n) for n=0..33.

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

Cf. A045636

Sequence in context: A090840 A227775 A204011 * A359492 A347357 A288069

Adjacent sequences: A359436 A359437 A359438 * A359440 A359441 A359442

Keyword

sign

Author

Robert Israel, Jan 02 2023

Status

approved