login
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
OFFSET
1,2
COMMENTS
a(n) <= a(n-1) + a(n-2) + a(n-3) - 2. - Charlie Neder, Feb 09 2019
LINKS
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
KEYWORD
nonn
AUTHOR
Ben Paul Thurston, Aug 06 2018
EXTENSIONS
a(24)-a(45) from Charlie Neder, Feb 09 2019
STATUS
approved