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 A236247 Sequence of distinct least squares such that the arithmetic mean of the first n squares is also a square. 1
 1, 49, 25, 121, 784, 196, 33124, 4900, 4, 4356, 2304324, 213444, 2371600, 379456, 87616, 360000, 3802500, 562500, 100, 532900, 5456896, 767376, 5934096, 992016, 9947716, 1350244, 32467204, 44100, 2414916, 10458756, 2683044 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Giovanni Resta, Table of n, a(n) for n = 1..200 FORMULA a(n) = A141391(n)^2 EXAMPLE a(1) = 1. a(2) is the smallest unused square such that (a(2)+a(1))/2 is a square. So, a(2) = 49. a(3) is the smallest unused square such that (a(3)+a(2)+a(1))/3 is a square. So, a(3) = 25. ...and so on. PROG (Python) def Sq(x): ..for n in range(10**15): ....if x == n**2: ......return True ....if x < n**2: ......return False ..return False def SqAve(init): ..print(init) ..lst = [] ..lst.append(init) ..n = 1 ..while n < 10**9: ....if n**2 not in lst: ......if Sq(((sum(lst)+n**2)/(len(lst)+1))): ........print(n**2) ........lst.append(n**2) ........n = 1 ......else: ........n += 1 ....else: ......n += 1 SqAve(1) CROSSREFS Cf. A019444, A141391. Sequence in context: A145583 A065787 A033369 * A226608 A027647 A221202 Adjacent sequences:  A236244 A236245 A236246 * A236248 A236249 A236250 KEYWORD nonn AUTHOR Derek Orr, Jan 20 2014 STATUS approved

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Last modified January 20 01:27 EST 2018. Contains 297938 sequences.