A061382 Decimal expansion of Pi/e.

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

Offset

1,3

References

Paul J. Nahin, "An Imaginary Tale, The Story of [Sqrt(-1)]," Princeton University Press, Princeton, NJ 1998, p. 188.

Links

Harry J. Smith, Table of n, a(n) for n = 1..20000

Z. A. Melzak, Infinite Products for Pi*e and Pi/e, The American Mathematical Monthly, Vol. 68, No. 1 (Jan., 1961), pp. 39-41 (3 pages).

Solution of Problem 11771, The American Mathematical Monthly, 121 (2014).

Formula

Equals A000796 / A001113.

Equals Integral_{-oo..oo} cos(x)/(1 + x^2) dx. - Robert G. Wilson v

Equals Integral_{-oo..oo} cos(x)/(1 + x^2)^2 dx. - Amiram Eldar, Jul 21 2020

From Robert FERREOL, Apr 02 2022: (Start)

Equals Integral_{-oo..oo} x*sin(x)/(1 + x^2) dx.

Equals 2*Integral_{-oo..oo} x*sin(x)/(1 + x^2)^2 dx. (End)

Equals Product_{k>=0} ((k + 1)/(k + 2))^(2*k + 3)*((2*k + 3)/(2*k + 1))^(2*k + 2). - Antonio Graciá Llorente, Mar 30 2024

Example

Pi/e ~= 1.15572734979092171791009318331269629912...

Mathematica

RealDigits[ Pi/E, 10, 110][[1]] (* Or *) RealDigits[ Integrate[ Cos[x]/(1 + x^2), {x, -Infinity, Infinity}], 10, 111][[1]] (* Robert G. Wilson v Jan 15 2004 *)

Prog

(PARI) { default(realprecision, 20080); x=Pi/exp(1); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b061382.txt", n, " ", d)) } \\ Harry J. Smith, Jul 22 2009

Crossrefs

Cf. A061666 (continued fraction for Pi/e).

Cf. A001113, A000796.

Sequence in context: A249649 A226571 A274030 * A113272 A222392 A049471

Adjacent sequences: A061379 A061380 A061381 * A061383 A061384 A061385

Keyword

cons,nonn,changed

Author

Jason Earls, Jun 08 2001

Status

approved