A227242 Decimal expansion of (e^gamma - 1)/e^gamma.

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

Offset

0,1

Comments

The value is equal to lim_{n->oo} (Sum_{d|n#, d>n} 1/phi(d))/(Sum_{d|n#} 1/phi(d)).

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Formula

From Alois P. Heinz, Feb 24 2022: (Start)

Equals 1 - exp(-gamma) = 1 - A080130.

Equals lim_{n->oo} A351901(n)/A000142(n). (End)

Example

(exp(gamma) - 1)/exp(gamma) = 0.438540516433114830175856785....

Maple

evalf(1-exp(-gamma), 120);  # Alois P. Heinz, Feb 24 2022

Mathematica

RealDigits[(E^EulerGamma - 1)/E^EulerGamma, 10, 50][[1]] (* G. C. Greubel, Oct 02 2017 *)

Prog

(Magma) E:=EulerGamma(RealField(105)); Reverse(Intseq(Floor(10^105*(Exp(E)-1)/Exp(E))))
(PARI) default(realprecision, 105); x=10*(exp(Euler)-1)/exp(Euler); for(n=1, 105, d=floor(x); x=(x-d)*10; print1(d, ", "));

Crossrefs

Cf. A000142, A001113, A001620, A073004, A080130, A351901.

Sequence in context: A361782 A353990 A092383 * A156028 A021232 A263616

Adjacent sequences: A227239 A227240 A227241 * A227243 A227244 A227245

Keyword

nonn,cons

Author

Arkadiusz Wesolowski, Oct 19 2013

Status

approved