A058287 Continued fraction for e^Pi.

23, 7, 9, 3, 1, 1, 591, 2, 9, 1, 2, 34, 1, 16, 1, 30, 1, 1, 4, 1, 2, 108, 2, 2, 1, 3, 1, 7, 1, 2, 2, 2, 1, 2, 3, 2, 166, 1, 2, 1, 4, 8, 10, 1, 1, 7, 1, 2, 3, 566, 1, 2, 3, 3, 1, 20, 1, 2, 19, 1, 3, 2, 1, 2, 13, 2, 2, 11, 3, 1, 2, 1, 7, 2, 1, 1, 1, 2, 1, 19, 1, 1, 12, 11, 1, 4, 1, 6, 1, 2, 18, 1, 2

Offset

0,1

Comments

"The transcendentality of e^{Pi} was proved in 1929." (Wells)

References

Jan Gullberg, "Mathematics, From the Birth of Numbers," W. W. Norton and Company, NY and London, 1997, page 86.

David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, Penguin Books, London, England, 1997, page 81.

Links

Harry J. Smith, Table of n, a(n) for n = 0..20000

V. Yu. Irkhin, Relations between e and Pi: Nilakantha's series and Stirling's formula, arXiv:2206.07174 [math.HO], 2022.

G. Xiao, Contfrac

Index entries for continued fractions for constants

Example

e^Pi = 23.140692632779269005... = 23 + 1/(7 + 1/(9 + 1/(3 + 1/(1 + ...)))). - Harry J. Smith, Apr 19 2009

Maple

with(numtheory): cfrac(evalf((exp(1))^(evalf(Pi)), 2560), 256, 'quotients');

Mathematica

ContinuedFraction[ E^Pi, 100]

Prog

(PARI) \p 300 contfrac(exp(1)^Pi)
(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(exp(1)^Pi); for (n=0, 20000, write("b058287.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Apr 19 2009

Crossrefs

Cf. A039661.

Sequence in context: A158514 A040511 A264350 * A122706 A096640 A040510

Adjacent sequences: A058284 A058285 A058286 * A058288 A058289 A058290

Keyword

cofr,nonn,easy

Author

Robert G. Wilson v, Dec 07 2000

Extensions

More terms from Jason Earls, Jun 21 2001

Status

approved