A141394 -id:A141394 - cp's OEIS frontend

A141391 a(n) is the smallest unused number such that the RMS (Root Mean Square) of a(1) through a(n) is an integer.

1, 7, 5, 11, 28, 14, 182, 70, 2, 66, 1518, 462, 1540, 616, 296, 600, 1950, 750, 10, 730, 2336, 876, 2436, 996, 3154, 1162, 5698, 210, 1554, 3234, 1638, 5382, 1872, 23088, 4368, 5934, 201, 4359, 77991, 7021, 13090, 4270, 12950, 74, 12802, 76466, 16954

Offset: 1

Andrew Weimholt, Jun 29 2008

nonn

Actual RMS values are given by A141392

			a(4) = 11. Sqrt(mean(1^2, 7^2, 5^2, k^2)) is an integer for k in {5,11,37}. We have already used 5 for a(3), so 11 is the smallest value available for a(4).

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

Cf. A141392, A141393, A141394, A140480.

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

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

Original entry on oeis.org

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

cp's OEIS Frontend

A141391 a(n) is the smallest unused number such that the RMS (Root Mean Square) of a(1) through a(n) is an integer.

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

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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.

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Author

Keywords

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