A096622 Harmonic expansion (or factorial expansion) of the Euler-Mascheroni constant.

0, 1, 0, 1, 4, 1, 4, 1, 3, 0, 2, 3, 0, 5, 14, 12, 16, 14, 7, 13, 18, 17, 19, 11, 22, 13, 13, 26, 12, 16, 2, 26, 1, 2, 28, 18, 3, 27, 31, 27, 9, 7, 37, 28, 13, 26, 2, 34, 29, 47, 49, 34, 39, 10, 0, 42, 1, 9, 42, 1, 32, 61, 23, 57, 42, 32, 2, 12, 32, 32, 48, 42, 49, 15, 14, 39, 48

Offset

1,5

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Harmonic Expansion

Index entries for factorial base representation

Formula

Sum_{n>=1} a(n)/n! = Euler gamma = A001620. - G. C. Greubel, Nov 26 2018

Example

Euler gamma = 0 + 1/2! + 0/3! + 1/4! + 4/5! + 1/6! + 4/7! + 1/8! + ...

Mathematica

With[{b = EulerGamma}, Table[If[n==1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]] (* G. C. Greubel, Nov 26 2018 *)

Prog

(PARI) default(realprecision, 250); b = Euler; for(n=1, 80, print1( if(n==1, floor(b), floor(n!*b) - n*floor((n-1)!*b)), ", ")) \\ G. C. Greubel, Nov 26 2018
(Magma) SetDefaultRealField(RealField(250));  [Floor(EulerGamma(250))] cat [Floor(Factorial(n)*EulerGamma(250)) - n*Floor(Factorial((n-1))*EulerGamma(250)) : n in [2..80]]; // G. C. Greubel, Nov 26 2018
(Sage)
b = euler_gamma;
def A096622(n):
    if (n==1): return floor(b)
    else: return expand(floor(factorial(n)*b) -n*floor(factorial(n-1)*b))
[A096622(n) for n in (1..80)] # G. C. Greubel, Nov 26 2018

Crossrefs

Cf. A001620 (decimal expansion), A002852 (continued fraction).

Sequence in context: A140704 A030748 A144865 * A331291 A080905 A010685

Adjacent sequences: A096619 A096620 A096621 * A096623 A096624 A096625

Keyword

nonn

Author

Eric W. Weisstein, Jul 01 2004

Status

approved