A141391 -id:A141391 - cp's OEIS frontend

A141392 a(n) = RMS( A141391(1) through A141391(n) ).

1, 5, 5, 7, 14, 14, 70, 70, 66, 66, 462, 462, 616, 616, 600, 600, 750, 750, 730, 730, 876, 876, 996, 996, 1162, 1162, 1582, 1554, 1554, 1638, 1638, 1872, 1872, 4368, 4368, 4419, 4359, 4359, 13209, 13090, 13090, 12950, 12950, 12802, 12802, 16954, 16954

Offset: 1

Andrew Weimholt, Jun 29 2008

nonn

			a(4) = 7 because first 4 terms of A141391 are 1,7,5,11 and sqrt(mean(1^2, 7^2, 5^2, 11^2)) = 7.

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

Cf. A141391, A141393, A141394, A140480.

lim=46;a141391={1};Do[i=1;Until[!MemberQ[a141391,i]&&IntegerQ[RootMeanSquare[Append[a141391,i]]],i++];AppendTo[a141391,i],{n,lim}];a[n_]:=RootMeanSquare[a141391[[1;;n]]];Array[a,lim] (* James C. McMahon, Jul 24 2025 *)

A141393 a(n) is the smallest number, larger than the previous, such that the RMS (Root Mean Square) of a(0) through a(n) is an integer.

Original entry on oeis.org

1, 7, 25, 33, 84, 294, 462, 750, 1155, 1705, 2431, 3017, 18130, 19684, 22052, 28996, 36907, 45925, 61957, 71309, 168889, 471799, 9998261, 11975939, 21577709, 29764925, 853783375, 1388314375, 1438304875, 2710683875, 2741707205, 62802867395, 72342543455

Offset: 0

Andrew Weimholt, Jun 29 2008

nonn

Actual RMS values are given by A141394.

Giovanni Resta, Table of n, a(n) for n = 0..100

Cf. A141391, A141392, A141394, A140480.

a(22)-a(32) from Giovanni Resta, Jan 22 2014

A141394 a(n) = RMS( A141393(0) through A141393(n) ).

Original entry on oeis.org

1, 5, 15, 21, 42, 126, 210, 330, 495, 715, 1001, 1295, 5180, 7252, 9028, 11356, 14195, 17535, 22211, 26887, 45241, 109871, 2087549, 3186259, 5326355, 7832875, 164490375, 308102375, 403718875, 634415375, 794973005, 11129622070, 16694433105, 22566503645

Offset: 0

Andrew Weimholt, Jun 29 2008

nonn

			a(3) = 21 because first 4 terms of A141393 are 1,7,25,33 and sqrt(mean(1^2, 7^2, 25^2, 33^2)) = 21.

Giovanni Resta, Table of n, a(n) for n = 0..100

Cf. A141391, A141392, A141393, A140480.

a(22)-a(33) from Giovanni Resta, Jan 22 2014

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

Original entry on oeis.org

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

Derek Orr, Jan 20 2014

nonn

			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.

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

Cf. A019444, A141391.

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)

a(n) = A141391(n)^2

cp's OEIS Frontend

A141392 a(n) = RMS( A141391(1) through A141391(n) ).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

A141393 a(n) is the smallest number, larger than the previous, such that the RMS (Root Mean Square) of a(0) through a(n) is an integer.

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

A141394 a(n) = RMS( A141393(0) through A141393(n) ).

Views

Author

Keywords

Examples

Links

Crossrefs

Extensions

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

Formula