A321290 Smallest positive number for which the 3rd power cannot be written as sum of 3rd powers of any subset of previous terms.

1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 17, 21, 22, 28, 29, 33, 38, 41, 48, 68, 70, 96, 124, 130, 158, 179, 239, 309, 310, 351, 468, 509, 640, 843, 900, 1251, 1576, 1640, 2305, 2444, 2989, 3410, 4575, 5758, 5998, 7490, 8602, 11657, 13017, 15553, 19150, 24411, 25365

Offset: 1

Author

Bert Dobbelaere, Nov 02 2018

Keywords

• nonn

Comments

a(n)^3 forms a sum-free sequence.

Examples

			a(10) = 13. 3rd powers of 14, 15 and 16 can be written as sums of 3rd powers of a subset of the terms {a(1)..a(10)}:
14^3 = 2^3 + 3^3 + 8^3 + 13^3,
15^3 = 4^3 + 5^3 + 7^3 + 8^3 + 10^3 + 11^3,
16^3 = 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 7^3 + 11^3 + 13^3,
17^3 cannot be written in this way, so a(11) = 17 is the next term.
		

Links

• Bert Dobbelaere, Table of n, a(n) for n = 1..100
• Wikipedia, Sum-free sequence

Crossrefs

Other powers: A321266 (2), A321291 (4), A321292 (5), A321293 (6)

Programs

Python

def findSum(nopt, tgt, a, smax, pwr):
    if nopt==0:
        return [] if tgt==0 else None
    if tgt<0 or tgt>smax[nopt-1]:
        return None
    rv=findSum(nopt-1, tgt - a[nopt-1]**pwr, a, smax, pwr)
    if rv!=None:
        rv.append(a[nopt-1])
    else:
        rv=findSum(nopt-1, tgt, a, smax, pwr)
    return rv
def A321290(n):
    POWER=3 ; x=0 ; a=[] ; smax=[] ; sumpwr=0
    while len(a)