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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 June 24 11:11 EDT 2017. Contains 288697 sequences.