A019741 Decimal expansion of e/4.

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

Offset

0,1

Comments

Also (with offset = 1) 2.5*e = Sum_{n>=1} A000326(n)/n!. - Richard R. Forberg, Jul 15 2013

Also abscissa of minimum of f(x) = 2*Pi/(4x)^(1/(2x)) = (Product_{k=1..x} Gamma(k/(2x))*Gamma(1 - k/(2x)))^(1/x). - Andrea Pinos, Nov 22 2023

Links

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

Jonathan Sondow and Huang Yi, New Wallis- and Catalan-Type Infinite Products for Pi, e and sqrt(2+sqrt(2)), The American Mathematical Monthly, Vol. 117, No. 10 (2010), pp. 912-917.

Index entries for transcendental numbers.

Formula

Equals Product_{k>=1} (((2^(k+1)-2)!!/(2^k-2)!!)/((2^(k+1)-1)!!/(2^k-1)!!))^(1/2^k) = (2/3)^(1/2) * (4*8/(5*7))^(1/4) * (8*10*12*14/(9*11*13*15))^(1/8) * ... (Sondow and Yi, 2010, p. 914, eq. (15)). - Amiram Eldar, Jul 02 2026

Example

0.679570457114761308840071867838165624439311773424989893741741906931019....

Mathematica

First[RealDigits[E/4, 10, 100]] (* Paolo Xausa, May 02 2024 *)

Prog

(PARI) default(realprecision, 20080); x=10*exp(1)/4; for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b019741.txt", n, " ", d)); \\ Harry J. Smith, May 10 2009

Crossrefs

Cf. A000326, A001113, A006085 (continued fraction).

Sequence in context: A048079 A011346 A155525 * A197634 A011482 A259929

Adjacent sequences: A019738 A019739 A019740 * A019742 A019743 A019744

Keyword

nonn,cons,changed

Author

N. J. A. Sloane

Status

approved