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A236415
Sequence of distinct least triangular numbers such that the arithmetic mean of the first n terms is also a triangular number. Initial term is 0.
0
0, 6, 3, 15, 741, 153, 25878, 3828, 16653, 253, 4753, 23653, 6328, 53956, 9730, 191890, 21115, 140185, 1225, 26335, 317206, 3160, 38503, 2108431, 37950, 121278, 1440905403, 53483653, 201733741, 58595725, 22663524351, 787786971, 23483020686, 1475521326
OFFSET
1,2
COMMENTS
Sequence is believed to be infinite. If a(31) exists, it will be greater than 10^10.
a(31)=22663524351. - Jon E. Schoenfield, Feb 07 2014
EXAMPLE
a(1) = 0.
a(2) must be a triangular number such that (a(1)+a(2))/2 is triangular. Thus, a(1) = 6.
a(3) must be a triangular number such that (a(1)+a(2)+a(3))/3 is triangular. Thus, a(3) = 3.
...and so on
PROG
(Python)
def Tri(x):
..for n in range(10**10):
....if x == n*(n+1)/2:
......return True
....if x < n*(n+1)/2:
......return False
..return False
def TriAve(init):
..print(init)
..lst = []
..lst.append(init)
..n = 1
..while n*(n+1)/2 < 10**10:
....if n*(n+1)/2 not in lst:
......if Tri(((sum(lst)+int(n*(n+1)/2))/(len(lst)+1))):
........print(int(n*(n+1)/2))
........lst.append(int(n*(n+1)/2))
........n = 1
......else:
........n += 1
....else:
......n += 1
CROSSREFS
Cf. A000217.
Sequence in context: A302350 A046879 A248267 * A267831 A328011 A231881
KEYWORD
nonn
AUTHOR
Derek Orr, Jan 25 2014
EXTENSIONS
More terms from Jon E. Schoenfield, Feb 07 2014
STATUS
approved