A236416 Sequence of distinct least positive triangular numbers such that the arithmetic mean of the first n terms is also a triangular number. Initial term is 1.

1, 55, 28, 136, 6670, 1378, 18528, 3828, 3, 3403, 39340, 75466, 12403, 179101, 24310, 6, 22791, 290703, 37675, 679195, 10, 66430, 550107865, 23981275, 188170300, 30548836, 2303731, 721801, 28474831, 311538241, 13741903, 37130653, 441149289778, 278657028

Offset

1,2

Comments

Sequence is believed to be infinite.

Links

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

Example

a(1) = 1.
a(2) is the least triangular number such that (a(1)+a(2))/2 is also triangular. So, a(2) = 55.
a(3) is the least triangular number such that (a(1)+a(2)+a(3))/3 is also triangular. So, a(3) = 28.
...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: A220134 A178509 A033375 * A214042 A112892 A232653

Adjacent sequences: A236413 A236414 A236415 * A236417 A236418 A236419

Keyword

nonn

Author

Derek Orr, Jan 25 2014

Extensions

Qualifier "positive" added to definition (otherwise, a(4) would be 0) by Jon E. Schoenfield, Feb 07 2014

a(33)-a(34) from Jon E. Schoenfield, Feb 07 2014

Status

approved