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 A321266 Smallest positive number for which the square cannot be written as sum of distinct squares of any subset of previous terms. 5
 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 32, 34, 48, 64, 68, 96, 128, 136, 192, 256, 272, 384, 512, 544, 768, 1024, 1088, 1536, 2048, 2176, 3072, 4096, 4352, 6144, 8192, 8704, 12288, 16384, 17408, 24576, 32768, 34816, 49152, 65536, 69632, 98304, 131072, 139264 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n)^2 = A226076(n) forms a sum-free sequence. LINKS Bert Dobbelaere, Table of n, a(n) for n = 1..89 Wikipedia, Sum-free sequence FORMULA a(n) = 2 * a(n-3) for n > 9 (conjectured). EXAMPLE 0^2 = 0 (sum of squares of the empty set). 1^2 cannot be written as sum of squares of the empty set, so a(1)=1. Suppose we determined all terms up to a(7)=12: 13^2 = 12^2 + 4^2 + 3^2, 14^2 = 12^2 + 6^2 + 4^2, 15^2 = 12^2 + 8^2 + 4^2 + 1^2. 16^2 cannot be written as sum of squares of distinct smaller terms, hence a(8)=16. 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 A321266(n): ....POWER=2 ; x=0 ; a=[] ; smax=[] ; sumpwr=0 ....while len(a)

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Last modified June 24 13:44 EDT 2021. Contains 345417 sequences. (Running on oeis4.)