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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
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
Sequence in context: A305045 A065787 A033369 * A299470 A226608 A027647
KEYWORD
nonn
AUTHOR
Derek Orr, Jan 20 2014
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)