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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.
0
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.
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
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