A068460 Factorial expansion of log(7) = Sum_{n>=1} a(n)/n!.

1, 1, 2, 2, 3, 3, 0, 3, 0, 8, 8, 2, 11, 1, 5, 11, 1, 7, 1, 11, 16, 12, 12, 13, 5, 4, 26, 19, 12, 20, 0, 18, 14, 22, 6, 29, 0, 27, 16, 23, 23, 23, 34, 27, 4, 27, 18, 0, 10, 27, 42, 24, 9, 16, 6, 52, 2, 38, 44, 30, 51, 61, 7, 19, 0, 45, 18, 51, 43, 54, 7, 15, 69, 44, 51, 9, 74, 5, 69

Offset: 1

Author

Benoit Cloitre, Mar 10 2002

Keywords

• nonn

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Index entries for factorial base representation of noninteger constants

Crossrefs

Cf. A016630 (decimal expansion), A016735 (continued fraction).

Cf. A067882 (log(2)), A322334 (log(3)), A322333 (log(5)), A068461 (log(11)).

Programs

Magma

SetDefaultRealField(RealField(250));  [Floor(Log(7))] cat [Floor(Factorial(n)*Log(7)) - n*Floor(Factorial((n-1))*Log(7)) : n in [2..80]]; // G. C. Greubel, Dec 05 2018

Maple

Digits:=200: a:=n->`if`(n=1,floor(log(7)),floor(factorial(n)*log(7))-n*floor(factorial(n-1)*log(7))); seq[120](a(n),n=1..80); # Muniru A Asiru, Dec 06 2018

Mathematica

With[{b = Log[7]}, Table[If[n == 1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]] (* G. C. Greubel, Dec 05 2018 *)

PARI

vector(30,n,if(n>1,t=t%1*n,t=log(7))\1) \\ Increase realprecision (e.g., \p500) to compute more terms. - M. F. Hasler, Nov 25 2018

PARI

default(realprecision, 250); b = log(7); for(n=1, 80, print1(if(n==1, floor(b), floor(n!*b) - n*floor((n-1)!*b)), ", ")) \\ G. C. Greubel, Dec 05 2018

Sage

def a(n):
    if (n==1): return floor(log(7))
    else: return expand(floor(factorial(n)*log(7)) - n*floor(factorial(n-1)*log(7)))
[a(n) for n in (1..80)] # G. C. Greubel, Dec 05 2018

Extensions

Name edited and keywords cons,easy removed by M. F. Hasler, Nov 25 2018