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%I #19 Feb 09 2019 11:09:17
%S 1,2,3,4,5,6,13,22,39,72,131,229,386,641,896,1164,1419,1855,2831,3545,
%T 5036,5750,8034,10022,12227,14377,17455,19951,24701,27197,36455,42303,
%U 49751,57232,65684,83879,94391,110073,124015,137442,156835,175130,209215,229396,242692
%N 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.
%C a(n) <= a(n-1) + a(n-2) + a(n-3) - 2. - _Charlie Neder_, Feb 09 2019
%H Charlie Neder, <a href="/A317778/b317778.txt">Table of n, a(n) for n = 1..70</a>
%e After 1,2,3,4,5,6: 7 cannot be the next term because 1+3+7 = 2+4+5.
%o (Python)
%o def u(series):
%o for i in range(0, len(series)):
%o for j in range(i+1, len(series)):
%o for k in range(j+1, len(series)):
%o for l in range(0, len(series)):
%o for m in range(l+1, len(series)):
%o for n in range(m+1, len(series)):
%o if len(set([i,j,k,l,m,n]))==6:
%o if series[i]+series[j]+series[k]==series[l]+series[m]+series[n]:
%o return False
%o return True
%o def a(series, n):
%o a = []
%o for i in range(0, len(series)):
%o a.append(series[i])
%o a.append(n)
%o return a
%o series = [1, 2, 3,4,5,6]
%o for i in range(7, 1000):
%o print(i)
%o nseries = a(series, i)
%o if u(nseries):
%o series.append(i)
%o print(series)
%o print(series)
%Y Cf. A011185.
%K nonn
%O 1,2
%A _Ben Paul Thurston_, Aug 06 2018
%E a(24)-a(45) from _Charlie Neder_, Feb 09 2019
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