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 A321291 Smallest positive number for which the 4th power cannot be written as sum of 4th powers of any subset of previous terms. 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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). LINKS Bert Dobbelaere, Table of n, a(n) for n = 1..104 Wikipedia, Sum-free sequence FORMULA a(n) = 2 * a(n-12) for n > 25 (conjectured). EXAMPLE 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. 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 A321291(n): ....POWER=4 ; x=0 ; a=[] ; smax=[] ; sumpwr=0 ....while len(a)

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Last modified June 14 16:56 EDT 2021. Contains 345037 sequences. (Running on oeis4.)