A067882 - OEIS

A067882

Factorial expansion of log(2) = Sum_{n>=1} a(n)/n!.

0, 1, 1, 0, 3, 1, 0, 3, 6, 2, 5, 4, 6, 11, 4, 11, 5, 12, 3, 5, 13, 2, 22, 6, 22, 13, 20, 7, 1, 0, 1, 20, 2, 6, 4, 1, 18, 14, 35, 2, 11, 31, 16, 19, 42, 36, 41, 0, 14, 31, 25, 43, 4, 13, 34, 53, 50, 57, 2, 30, 12, 25, 45, 24, 2, 39, 57, 51, 30, 41, 65, 15, 9, 55, 23, 4, 35, 18, 77, 43

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OFFSET

1,5

LINKS

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

Index entries for factorial base representation of noninteger constants

FORMULA

a(n) = floor(n!*log(2)) - n*floor((n-1)!*log(2)).

EXAMPLE

log(2) = 0 + 1/2! + 1/3! + 0/4! + 3/5! + 1/6! + 0/7! + 3/8! + 6/9! + ...

MATHEMATICA

With[{b = Log[2]}, 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 = log(2); 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(Log(2))] cat [Floor(Factorial(n)*Log(2)) - n*Floor(Factorial((n-1))*Log(2)) : n in [2..80]]; // G. C. Greubel, Nov 26 2018

(Sage)

def A067882(n):

if (n==1): return floor(log(2))

else: return expand(floor(factorial(n)*log(2)) - n*floor(factorial(n-1)*log(2)))

[A067882(n) for n in (1..80)] # G. C. Greubel, Nov 26 2018

CROSSREFS

Cf. A002162 (decimal expansion), A016730 (continued fraction).

Cf. A322334 (log(3)), A322333 (log(5)), A068460 (log(7)), A068461 (log(11)).

Sequence in context: A104556 A116089 A122016 * A215771 A110033 A213666

Adjacent sequences: A067879 A067880 A067881 * A067883 A067884 A067885

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Mar 10 2002

STATUS

approved