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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 21 18:26 EDT 2019. Contains 326168 sequences. (Running on oeis4.)