A016634 - OEIS

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,1

REFERENCES

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.

LINKS

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

FORMULA

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

EXAMPLE

2.3978952727983705440619435779651292998217068539374171752185677...

MATHEMATICA

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

PROG

(PARI) 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

CROSSREFS

Cf. A016739 Continued fraction.

Sequence in context: A357053 A340442 A199963 * A244257 A171054 A205860

Adjacent sequences: A016631 A016632 A016633 * A016635 A016636 A016637

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane

STATUS

approved