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A236247
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Sequence of distinct least squares such that the arithmetic mean of the first n squares is also a square.
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1
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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
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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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.
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PROG
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(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)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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