A321291 Smallest positive number for which the 4th power cannot be written as sum of 4th powers of any subset of previous terms.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 32, 34, 36, 38, 40, 42, 44, 46, 48, 52, 54, 56, 64, 68, 72, 76, 80, 84, 88, 92, 96, 104, 108, 112, 128, 136, 144, 152, 160, 168, 176, 184, 192, 208, 216, 224, 256

Offset: 1

Author

Bert Dobbelaere, Nov 02 2018

Keywords

• nonn

Comments

a(n)^4 forms a sum-free sequence.

It is noteworthy that the terms of this sequence increase slower than those of similar sequences for smaller (A321266, A321290) but also larger powers (A321292, A321293).

Examples

			The smallest number > 0 that is not in the sequence is 15, because
    15^4 = 4^4 + 6^4 + 8^4 + 9^4 + 14^4.
		

Links

• Bert Dobbelaere, Table of n, a(n) for n = 1..104
• Wikipedia, Sum-free sequence

Crossrefs

Other powers: A321266 (2), A321290 (3), 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 A321291(n):
    POWER=4 ; x=0 ; a=[] ; smax=[] ; sumpwr=0
    while len(a)
				

Formula

a(n) = 2 * a(n-12) for n > 25 (conjectured).