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A322604 Factorial expansion of exp(gamma) = Sum_{n>=1} a(n)/n! with a(n) as large as possible. 0
1, 1, 1, 2, 3, 4, 2, 4, 7, 5, 6, 5, 12, 1, 12, 9, 0, 7, 4, 14, 10, 17, 2, 14, 23, 4, 2, 2, 16, 2, 10, 18, 23, 26, 26, 26, 24, 1, 17, 26, 18, 12, 0, 15, 42, 34, 39, 33, 20, 18, 40, 43, 12, 47, 51, 10, 50, 35, 14, 23, 16, 1, 55, 41, 34, 29, 14, 41, 35, 60, 53, 45, 61, 35, 49, 73, 13, 13, 57, 59 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Gamma is the Euler-Mascheroni constant (A001620).

LINKS

Table of n, a(n) for n=1..80.

Eric Weisstein's World of Mathematics, Harmonic Expansion

Index entries for factorial base representation

FORMULA

Sum_{n>=1} a(n)/n! = exp(gamma) = A073004.

EXAMPLE

exp(gamma) = 1 + 1/2! + 1/3! + 2/4! + 3/5! + 4/6! + 2/7! + 4/8! + ...

MAPLE

Digits:=200: a:=n->`if`(n=1, floor(exp(gamma)), floor(factorial(n)*exp(gamma))-n*floor(factorial(n-1)*exp(gamma))): seq(a(n), n=1..100); # Muniru A Asiru, Dec 20 2018

MATHEMATICA

With[{b = Exp[EulerGamma]}, Table[If[n==1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]]

PROG

(PARI) default(realprecision, 250); b = exp(Euler); for(n=1, 80, print1( if(n==1, floor(b), floor(n!*b) - n*floor((n-1)!*b)), ", "))

CROSSREFS

Cf. A073004 (decimal expansion), A094644 (continued fraction), A001620 (Euler-Mascheroni constant).

Sequence in context: A043264 A268444 A117826 * A173229 A191248 A323156

Adjacent sequences:  A322601 A322602 A322603 * A322605 A322606 A322607

KEYWORD

nonn

AUTHOR

Tristan Cam, Dec 20 2018

STATUS

approved

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Last modified September 27 07:39 EDT 2021. Contains 347672 sequences. (Running on oeis4.)