A016739 -id:A016739 - cp's OEIS frontend

A016634 Decimal expansion of log(11).

2, 3, 9, 7, 8, 9, 5, 2, 7, 2, 7, 9, 8, 3, 7, 0, 5, 4, 4, 0, 6, 1, 9, 4, 3, 5, 7, 7, 9, 6, 5, 1, 2, 9, 2, 9, 9, 8, 2, 1, 7, 0, 6, 8, 5, 3, 9, 3, 7, 4, 1, 7, 1, 7, 5, 2, 1, 8, 5, 6, 7, 7, 0, 9, 1, 3, 0, 5, 7, 3, 6, 2, 3, 9, 1, 3, 2, 3, 6, 7, 1, 3, 0, 7, 5, 0, 5, 4, 7, 0, 8, 0, 0, 2, 6, 3, 4, 7, 9

Offset: 1

N. J. A. Sloane

			2.3978952727983705440619435779651292998217068539374171752185677...

Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 2.

Harry J. Smith, Table of n, a(n) for n = 1..20000
Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Index entries for transcendental numbers

Cf. A016739 Continued fraction.

RealDigits[Log[11], 10, 120][[1]] (* Harvey P. Dale, Mar 09 2014 *)

default(realprecision, 20080); x=log(11); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b016634.txt", n, " ", d)); \\ Harry J. Smith, May 16 2009

log(11) = 2*Sum_{n >= 1} 1/(n*P(n, 6/5)*P(n-1, 6/5)), where P(n, x) denotes the n-th Legendre polynomial. The first 20 terms of the series gives the approximation log(11) = 2.3978952727(47...), correct to 10 decimal places. - Peter Bala, Mar 19 2024

Equals 2*(log 2+log 5 -log 3)+Sum_{k>=1} (-1)^k/(k*100^k). - R. J. Mathar, Jun 10 2024

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

Original entry on oeis.org

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

Benoit Cloitre, Mar 10 2002

nonn

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

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)).

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

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 *)

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

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

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

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

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A016634 Decimal expansion of log(11).

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

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