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, 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

Links

Table of n, a(n) for n=1..34.

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

Adjacent sequences: A236412 A236413 A236414 * A236416 A236417 A236418

Keyword

nonn

Author

Derek Orr, Jan 25 2014

Extensions

More terms from Jon E. Schoenfield, Feb 07 2014

Status

approved