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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 (list; graph; refs; listen; history; text; internal format)
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 A231881 A229005

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

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Last modified August 24 13:48 EDT 2019. Contains 326279 sequences. (Running on oeis4.)