A117191 Decimal expansion of 4^(1/Pi).

1, 5, 5, 4, 6, 8, 2, 2, 7, 5, 4, 8, 2, 1, 0, 0, 0, 8, 9, 8, 7, 0, 2, 3, 2, 0, 8, 0, 7, 8, 2, 8, 0, 4, 0, 0, 2, 0, 6, 0, 4, 4, 7, 3, 0, 6, 2, 6, 5, 6, 6, 1, 3, 7, 9, 0, 9, 8, 9, 2, 0, 2, 0, 4, 3, 3, 2, 8, 7, 7, 9, 4, 1, 5, 2, 9, 3, 2, 8, 0, 5, 3, 6, 5, 1, 1, 3, 9, 7, 6, 3, 8, 2, 3, 1, 8, 7, 4, 8, 9, 3, 6, 3, 0, 5

Offset

1,2

Comments

Gosper found that lim[n approaches infinity] Prod[i=n..2n] Pi/2 arctan i = 4^(1/Pi) ~ 1.554682275...

References

Gosper, R. W. math-fun(AT)cs.arizona.edu posting, Sept. 1996.

Gosper, R. W. "a product." math-fun(AT)cs.arizona.edu posting, Sept. 27, 1996.

Links

Table of n, a(n) for n=1..105.

R. W. Gosper, Some identities

Eric Weisstein's World of Mathematics, Pi Formulas.

Example

1.5546822754821000898702320807828040020604473062656613790989...

Mathematica

RealDigits[4^(1/Pi), 10, 120][[1]] (* Harvey P. Dale, Sep 05 2019 *)

Prog

(Macsyma) 'limit(funmake_no_simp(".", [%pi/2/atan(n), %pi/2/atan(n+1), "", "", %pi/2/atan(2*n)]), n, inf)=4^(1/%pi)

Crossrefs

Sequence in context: A257872 A180138 A094245 * A011189 A261346 A011409

Adjacent sequences: A117188 A117189 A117190 * A117192 A117193 A117194

Keyword

cons,easy,nonn

Author

Jonathan Vos Post, Apr 21 2006

Extensions

More terms from Eric W. Weisstein, May 01 2006

Edited by N. J. A. Sloane, Jul 01 2008 at the suggestion of R. J. Mathar

Status

approved