A348132 a(n) is the denominator of the relativistic sum of n velocities of 1/n, in units where the speed of light is 1.

1, 5, 9, 353, 275, 66637, 18571, 24405761, 2215269, 14712104501, 411625181, 13218256749601, 109949704423, 16565151205544957, 39931933598775, 27614800115689879553, 18928981513351817, 59095217374989483261925, 11350851717672992089, 157904201452248753415276001

Offset: 1

Author

Amiram Eldar, Oct 01 2021

Keywords

• nonn
• frac

Examples

			For n = 2, the sum of two velocities of 1/2 is (1/2 + 1/2)/(1 + (1/2)*(1/2)) = 4/5, thus a(2) = 5.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..387
• Wikipedia, Velocity-addition formula.

Crossrefs

Cf. A348051, A348052, A348131 (numerators).

Programs

Mathematica

f[n_] := Module[{s = 1/n}, Do[s = (s + 1/n)/(1 + s/n), {k, 1, n - 1}]; s]; Denominator @ Array[f, 20]

Formula

a(2n-1) = n^(2n-1) + (n-1)^(2n-1) and a(2n) = ((2n+1)^(2n) + (2n-1)^(2n)) / 2. - Thomas Ordowski, Feb 12 2022