A321293 Smallest positive number for which the 6th power cannot be written as sum of distinct 6th powers of any subset of previous terms.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 29, 30, 31, 33, 34, 42, 43, 51, 57, 60, 61, 71, 74, 88, 91, 99, 112, 116, 117, 132, 152, 153, 176, 203, 228, 244, 256, 281, 293, 345, 392, 439, 441, 529, 594, 627

Offset: 1

Author

Bert Dobbelaere, Nov 02 2018

Keywords

• nonn

Comments

a(n)^6 forms a sum-free sequence.

Examples

			The smallest number > 0 that is not in the sequence is 25, because 25^6 = 1^6 + 2^6 + 3^6 + 5^6 + 6^6 + 7^6 + 8^6 + 9^6 + 10^6 + 12^6 + 13^6 + 15^6 + 16^6 + 17^6 + 18^6 + 23^6.
		

Links

• Bert Dobbelaere, Table of n, a(n) for n = 1..150
• Wikipedia, Sum-free sequence

Crossrefs

Other powers: A321266 (2), A321290 (3), A321291 (4), A321292 (5).

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 A321293(n):
    POWER=6 ; x=0 ; a=[] ; smax=[] ; sumpwr=0
    while len(a)