A236247 Sequence of distinct least squares such that the arithmetic mean of the first n squares is also a square.

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

Offset: 1

Author

Derek Orr, Jan 20 2014

Keywords

• nonn

Examples

			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.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A019444, A141391.

Programs

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)

Formula

a(n) = A141391(n)^2