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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 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.)