Smallest positive number s(n) such that s(n) and all greater numbers can be expressed as the sum of n-th powers of distinct primes.

1, 7, 17164, 1866001, 340250525753

0

This is sequence A121571 plus 1. The first four terms are listed in Table 3 in the paper by Fuller and Nichols. The last term required 150 hours on a PC having 64 GB of RAM. For more information see sequences S001072 and S001073.

T. D. Noe, Plot of 5 terms

Chris Fuller and Robert H. Nichols, Jr., Generalized Anti-Waring Numbers, J. of Integer Sequences, Vol. 18 (2015) Article 15.10.5

Cf. A121571, S001072, S001073.

nonn,hard

T. D. Noe, Oct 03 2017