A001698 -id:A001698 - cp's OEIS frontend

A001675 a(n) = round(sqrt( 2*Pi )^n).

1, 3, 6, 16, 39, 99, 248, 622, 1559, 3907, 9793, 24546, 61529, 154230, 386598, 969056, 2429064, 6088760, 15262259, 38256810, 95895601, 240374624, 602529829, 1510318305, 3785806568, 9489609784, 23786924201, 59624976768, 149457652642, 374634777972

Offset: 0

N. J. A. Sloane

nonn

Cf. A001674 (floor sqrt(2 Pi)^n), A001698 (ceiling sqrt(2 Pi)^n).

Cf. A017911 (round sqrt(2)), A000227 (round e^n), A002160 (round Pi^n).

Table[Floor[Sqrt[2*Pi]^n + 1/2], {n, 0, 50}] (* T. D. Noe, Aug 09 2012 *)
Round[(Sqrt[2*Pi])^Range[0,30] ] (* Harvey P. Dale, Jun 05 2018 *)

apply( a(n)=(2*Pi)^(n/2)\/1, [0..40]) \\ M. F. Hasler, May 29 2018

A305289 Powers of 2*Pi, rounded to the nearest integer.

Original entry on oeis.org

1, 6, 39, 248, 1559, 9793, 61529, 386598, 2429064, 15262259, 95895601, 602529829, 3785806568, 23786924201, 149457652642, 939070127125, 5900351625162, 37073002638414, 232936545470713, 1463583480006755, 9195966217409213, 57779959822545404, 363042194606444109, 2281061383037441740

Offset: 0

M. F. Hasler, May 29 2018

nonn

Index entries of sequences related to powers of irrational constants.

Cf. A001674 (floor(sqrt(2 Pi)^n)), A001675 (round sqrt(2 Pi)^n), A001698 (ceiling sqrt(2 Pi)^n), A017911 (round sqrt(2)^n), A000227 (round e^n), A002160 (round Pi^n).

Round[(2Pi)^Range[0,30]] (* Harvey P. Dale, Aug 12 2021 *)

PARI
```
apply( a(n)=(2*Pi)^n\/1, [0..40])
```

a(n) = round((2 Pi)^n) = A001675(2*n) >= A001674(2n).

cp's OEIS Frontend

A001675 a(n) = round(sqrt( 2*Pi )^n).

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