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 A321293 Smallest positive number for which the 6th power cannot be written as sum of distinct 6th powers of any subset of previous terms. 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n)^6 forms a sum-free sequence. LINKS Bert Dobbelaere, Table of n, a(n) for n = 1..150 Wikipedia, Sum-free sequence EXAMPLE 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. PROG (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)

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Last modified May 12 07:28 EDT 2021. Contains 343821 sequences. (Running on oeis4.)