A068461 Factorial, or factoradic, expansion of log(11) = Sum_{n>=1} a(n)/n!, with a(n) as large as possible.

2, 0, 2, 1, 2, 4, 3, 3, 1, 2, 4, 0, 3, 13, 1, 12, 12, 13, 1, 16, 16, 0, 16, 12, 10, 9, 1, 23, 3, 22, 0, 28, 11, 14, 23, 16, 0, 14, 6, 1, 1, 14, 4, 25, 43, 0, 29, 10, 41, 19, 47, 14, 0, 51, 10, 47, 37, 45, 46, 56, 57, 45, 10, 32, 61, 15, 9, 67, 5, 9, 22, 25, 65, 56, 24, 12, 71, 9, 57

Offset: 1

Author

Benoit Cloitre, Mar 10 2002

Keywords

• nonn

Examples

			log(11) = 2 + 0/2! + 2/3! + 1/4! + 2/5! + 4/6! + 3/7! + 3/8! + 1/9! + ...
		

Links

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

Crossrefs

Cf. A016634 (decimal expansion), A016739 (continued fraction).

Cf. A007514 vs. A075874 for factoradic expansion.

Cf. A067882 (log(2)), A322334 (log(3)), A322333 (log(5)), A068460 (log(7)).

Programs

Magma

SetDefaultRealField(RealField(250));  [Log(11)] cat [Floor(Factorial(n)*Log(11)) - n*Floor(Factorial((n-1))*Log(11)) : n in [2..80]]; // G. C. Greubel, Dec 05 2018

Mathematica

With[{b = Log[11]}, 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(11))\1) \\ Increase realprecision (e.g., \p500) to compute more terms. - M. F. Hasler, Nov 25 2018

PARI

default(realprecision, 250); b = log(11); 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(11))
    else: return expand(floor(factorial(n)*log(11)) - n*floor(factorial(n-1)*log(11)))
[a(n) for n in (1..80)] # G. C. Greubel, Dec 05 2018

Extensions

Name edited and keyword cons,easy removed by M. F. Hasler, Nov 26 2018