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 A321290 Smallest positive number for which the 3rd power cannot be written as sum of 3rd powers of any subset of previous terms. 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n)^3 forms a sum-free sequence. LINKS Bert Dobbelaere, Table of n, a(n) for n = 1..100 Wikipedia, Sum-free sequence EXAMPLE 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. 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 A321290(n): ....POWER=3 ; x=0 ; a=[] ; smax=[] ; sumpwr=0 ....while len(a)

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Last modified June 12 19:17 EDT 2021. Contains 344959 sequences. (Running on oeis4.)