A001672 a(n) = floor(Pi^n).

1, 3, 9, 31, 97, 306, 961, 3020, 9488, 29809, 93648, 294204, 924269, 2903677, 9122171, 28658145, 90032220, 282844563, 888582403, 2791563949, 8769956796, 27551631842, 86556004191, 271923706893, 854273519913, 2683779414317, 8431341691876, 26487841119103

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 0..300

Crossrefs

See also A002160: closest integer to Pi^n.

Cf. A001673.

Programs

Mathematica

Table[Floor[Pi^n], {n, 0, 50}] (* Vladimir Joseph Stephan Orlovsky, Dec 12 2008 *)

PARI

A001672(n)=Pi^n\1 \\ An error message will say so if default(realprecision) must be increased. - M. F. Hasler, May 27 2018

Formula

a(n)^(1/n) converges to Pi because |1 - a(n)/Pi^n| = |Pi^n - a(n)|/Pi^n < 1/Pi^n and so a(n)^(1/n) = (Pi^n*(1+o(1)))^(1/n) = Pi*(1+o(1)). - Hieronymus Fischer, Jan 22 2006