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, 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

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