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 A317778 Starting with 1,2,3,4,5,6: a(n) is the next smallest number greater than a(n-1) such that a[i] + a[j] + a[k] != a[x] + a[y] + a[z] for 1 <= i,j,k,x,y,z <= n all distinct. 1
 1, 2, 3, 4, 5, 6, 13, 22, 39, 72, 131, 229, 386, 641, 896, 1164, 1419, 1855, 2831, 3545, 5036, 5750, 8034, 10022, 12227, 14377, 17455, 19951, 24701, 27197, 36455, 42303, 49751, 57232, 65684, 83879, 94391, 110073, 124015, 137442, 156835, 175130, 209215, 229396, 242692 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) <= a(n-1) + a(n-2) + a(n-3) - 2. - Charlie Neder, Feb 09 2019 LINKS Charlie Neder, Table of n, a(n) for n = 1..70 EXAMPLE After 1,2,3,4,5,6: 7 cannot be the next term because 1+3+7 = 2+4+5. PROG (Python) def u(series):     for i in range(0, len(series)):         for j in range(i+1, len(series)):             for k in range(j+1, len(series)):                 for l in range(0, len(series)):                     for m in range(l+1, len(series)):                         for n in range(m+1, len(series)):                             if len(set([i, j, k, l, m, n]))==6:                                 if series[i]+series[j]+series[k]==series[l]+series[m]+series[n]:                                     return False     return True def a(series, n):     a = []     for i in range(0, len(series)):         a.append(series[i])     a.append(n)     return a series = [1, 2, 3, 4, 5, 6] for i in range(7, 1000):     print(i)     nseries = a(series, i)     if u(nseries):         series.append(i)         print(series) print(series) CROSSREFS Cf. A011185. Sequence in context: A276529 A200330 A121433 * A259541 A274838 A200331 Adjacent sequences:  A317775 A317776 A317777 * A317779 A317780 A317781 KEYWORD nonn AUTHOR Ben Paul Thurston, Aug 06 2018 EXTENSIONS a(24)-a(45) from Charlie Neder, Feb 09 2019 STATUS approved

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Last modified May 19 06:57 EDT 2019. Contains 323386 sequences. (Running on oeis4.)