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

0,2

Links

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

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

Mathematica

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

Prog

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

Crossrefs

See also A002160: closest integer to Pi^n.

Cf. A001673.

Sequence in context: A034550 A018370 A183519 * A138281 A049416 A148959

Adjacent sequences: A001669 A001670 A001671 * A001673 A001674 A001675

Keyword

nonn

Author

N. J. A. Sloane

Status

approved