A068461 - OEIS

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

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OFFSET

1,1

LINKS

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

Index entries for factorial base representation of noninteger constants

EXAMPLE

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

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 *)

PROG

(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

(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

(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

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)).

Sequence in context: A182893 A206298 A076608 * A130456 A222049 A071497

Adjacent sequences: A068458 A068459 A068460 * A068462 A068463 A068464

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Mar 10 2002

EXTENSIONS

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

STATUS

approved