A321292 Smallest positive number for which the 5th power cannot be written as sum of distinct 5th powers of any subset of previous terms.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 25, 26, 27, 28, 30, 37, 43, 44, 55, 57, 64, 77, 82, 90, 97, 112, 116, 119, 154, 156, 178, 202, 227, 269, 309, 335, 371, 397, 442, 516, 604, 643, 722, 774, 815, 1000, 1115, 1308, 1503

Offset: 1

Author

Bert Dobbelaere, Nov 02 2018

Keywords

• nonn

Comments

a(n)^5 forms a sum-free sequence.

Examples

			The smallest number > 0 that is not in the sequence is 12, because
12^5 = 4^5 + 5^5 + 6^5 + 7^5 + 9^5 + 11^5.
		

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), 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 A321292(n):
    POWER=5 ; x=0 ; a=[] ; smax=[] ; sumpwr=0
    while len(a)