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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

%I

%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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Last modified June 19 06:47 EDT 2019. Contains 324218 sequences. (Running on oeis4.)