A016650 Decimal expansion of log(27).

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Examples

			3.295836866004329074185735710767577113942471673468248355204083000912482... - _Harry J. Smith_, May 20 2009
		

References

• M. Abramowitz and I. 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
• M. Abramowitz and I. 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

Crossrefs

Cf. A016455 (continued fraction).

Programs

Mathematica

RealDigits[Log[27],10,120][[1]] (* Harvey P. Dale, May 07 2012 *)

PARI

default(realprecision, 20080); x=log(27); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b016650.txt", n, " ", d)); \\ Harry J. Smith, May 20 2009

Formula

Log(27) = Integral_{x = 0..oo} sin(4*x)^3/x^2 dx. - Peter Bala, Nov 04 2019

From Peter Bala, Feb 27 2024: (Start)

Equals 4 - 2*Sum_{k >= 0} 1/((2*k + 1)*(2*k + 3)*4^k).

Continued fraction: 4 - 16/(24 - 96/(84 - 1440/(186 - ... - 16*n*(n + 1)(4*n^2 - 1)/((2*(n + 1)*(10*n + 11)) - ... )))). (End)

Equals 3*A002391. - R. J. Mathar, Jul 22 2025