A359448 a(n) is the least number that is the sum of two cubes of primes and is 2^n times an odd number.

35, 54, 468, 152, 16, 9056, 81088, 527744, 4532992, 33900032, 268684288, 2148866048, 17185288192, 137439174656, 1099611160576, 8797884612608, 70369850097664, 562950041894912, 4503607335190528, 36028810622664704, 288230406982991872, 2305843633483415552, 18446744212436156416, 147573952867129622528

Offset

0,1

Comments

a(n) is the least member k of A086119 such that A007814(k) = n.

a(n) <= A359447(n) if A359447(n) > 0.

Since p^3 + q^3 = (p+q)*(p^2 - p*q + q^2), except for n=4 we must have A007814(p+q) = n.

There is no analogous sequence for squares, because if p and q are odd primes p^2 + q^2 == 2 (mod 4).

Links

Robert Israel, Table of n, a(n) for n = 0..1000

Example

a(0) = 35 = 2^3 + 3^3 = 2^0 * 35 with 2 and 3 prime and 35 odd.
a(1) = 54 = 3^3 + 3^3 = 2^1 * 27 with 3 and 3 prime and 27 odd.
a(2) = 468 = 5^3 + 7^3 = 2^2 * 117 with 5 and 7 prime and 117 odd.
a(3) = 152 = 3^3 + 5^3 = 2^3 * 19 with 3 and 5 prime and 19 odd.
a(4) = 16 = 2^3 + 2^3 = 2^4 * 1 with 2 and 2 prime and 1 odd.

Maple

f:= proc(n) local p, q, b, t, r;
  r:= infinity;
  for b from 1 by 2 while 2^(3*n-2)*b^3 < r do
    t:= 2^n*b;
    p:= nextprime(t/2);
    while p > 3 do
      p:= prevprime(p);
      q:= t-p;
      if p^3 + q^3 > r then break fi;
      if isprime(q) then r:= p^3 + q^3; break fi;
    od
  od;
    r
end proc:
f(0):= 35: f(4):= 16:
map(f, [$0..30]);

Crossrefs

Cf. A007814, A086119, A359447.

Sequence in context: A043135 A039312 A043915 * A355812 A318572 A171082

Adjacent sequences: A359445 A359446 A359447 * A359449 A359450 A359451

Keyword

nonn

Author

Robert Israel, Jan 01 2023

Status

approved