A359447 a(n) is the least number that is the sum of two cubes of primes and is 2^n times an odd prime, or -1 if there is no such number.

-1, -1, 152, 2224, 9056, 108736, -1, 4532992, 34674176, 268684288, 2280249344, 18693763072, 138890141696, 1111848828928, 8803419521024, 70375767212032, 564861779443712, 4507018424221696, 36030079546425344, 288238419152207872, 2305850719072157696, 18446757709572210688, 147573952867129622528

Offset: 1

Author

Robert Israel, Jan 01 2023

Keywords

• sign

Comments

a(n) is the least term of A086119 such that a(n)/2^n is an odd prime, or -1 if there is no such term.

Since p^3 + q^3 = (p+q)*(p^2 - p*q + q^2), we must have p+q = 2^n, and p^2 - p*q + q^2 an odd prime.

Is a(n) > 0 for all n > 7?

Examples

			a(3) = 152 because 3^3 + 5^3 = 152 = 2^3 * 19, 3 and 5 are primes and 19 is odd, and no smaller number works.
		

Crossrefs

Cf. A086119, A359448.

Programs

Maple

f:= proc(n) local p,q,t;
  t:= 2^n; p:= nextprime(t/2);
  while p > 2 do
    p:= prevprime(p);
    q:= t - p;
    if isprime(q) and isprime(p^2 - p*q + q^2) then return p^3 + q^3 fi
  od;
-1
end proc:
map(f, [$1..20]);