1,1

By parity, there must be an odd number of odds in the sum. Hence this sequence is the union of primes which are the sum of five odd cubes (such as 5 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3); primes which are the sum of the cube of two even numbers and the cubes of three odd numbers (such as 19 = 1^3 + 1^3 + 1^3 + 2^3 + 2^3); and the primes which are the sum of the cube of an odd number and the cubes of four even numbers (such as 59 = 3^3 + 2^3 + 2^3 + 2^3 + 2^3). A subset of this sequence is the primes which are the sum of the cubes of five distinct primes (i.e. of the form p^3 + q^3 + r^3 + s^3 + t^3 for p, q, r, s, t distinct odd primes) such as 105649 = 3^3 + 5^3 + 7^3 + 11^3 + 47^3. No prime can be the sum of two cubes (by factorization of the sum of two cubes).

A000040 INTERSECTION A003328.

a(1) = 5 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3.

a(2) = 19 = 1^3 + 1^3 + 1^3 + 2^3 + 2^3.

a(3) = 1^3 + 1^3 + 1^3 + 1^3 + 3^3.

a(4) = 59 = 3^3 + 2^3 + 2^3 + 2^3 + 2^3.

Cf. A000040, A003328.

Sequence in context: A115103 A045457 A138242 this_sequence A031019 A031041 A029523

Adjacent sequences: A122726 A122727 A122728 this_sequence A122730 A122731 A122732

easy,nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), Sep 23 2006