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

Author

Ben Paul Thurston, Aug 06 2018

Keywords

• nonn

Comments

a(n) <= a(n-1) + a(n-2) + a(n-3) - 2. - Charlie Neder, Feb 09 2019

Examples

			After 1,2,3,4,5,6: 7 cannot be the next term because 1+3+7 = 2+4+5.
		

Links

• Charlie Neder, Table of n, a(n) for n = 1..70

Crossrefs

Cf. A011185.

Programs

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)

Extensions

a(24)-a(45) from Charlie Neder, Feb 09 2019