A094227 A prime-power sequence based on Gaussian asymptotic function.

0, 1, 3, 5, 8, 10, 13, 15, 18, 21, 24, 27, 30, 33, 36, 40, 43, 46, 50, 53, 57, 61, 64, 68, 72, 75, 79, 83, 87, 91, 95, 99, 102, 106, 111, 115, 119, 123, 127, 131, 135, 139, 144, 148, 152, 157, 161, 165, 170, 174, 178, 183, 187, 192, 196, 201, 205, 210, 214, 219, 223

Offset

3,3

Links

Table of n, a(n) for n=3..63.

Formula

a(n) = Floor[N[n*(n-1)^s(n)]] with s(n)=(Log[g[n]]-Log[n])/Log[n-1] and g[n]=(n*Pi*Log[n]-Sqrt[n^2*Pi+2*Pi^2*n])/Pi.

a(n) ~ n log n. - Charles R Greathouse IV, Aug 24 2022

Mathematica

g[n_]=(n*Pi*Log[n]-Sqrt[n^2*Pi+2*Pi^2*n])/Pi f[n_]=(Log[g[n]]-Log[n])/Log[n-1] a=Table[Floor[N[n*(n-1)^fa[n]]], {n, 3, 200}]

Prog

(PARI) s(n)=log(log(n) - sqrt(1/Pi+2/n))/log(n-1)
a(n)=n*(n-1)^s(n)\1 \\ Charles R Greathouse IV, Aug 24 2022

Crossrefs

Sequence in context: A332102 A047218 A029919 * A085225 A080370 A175540

Adjacent sequences: A094224 A094225 A094226 * A094228 A094229 A094230

Keyword

nonn,less

Author

Roger L. Bagula, May 28 2004

Status

approved