A016632 Decimal expansion of log(9).

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Examples

			2.197224577336219382790490473845051409294981115645498903469388667274988...
		

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. A016737 Continued fraction.

Programs

Mathematica

First[RealDigits[Log[9], 10, 100]] (* Paolo Xausa, Mar 21 2024 *)

PARI

default(realprecision, 20080); x=log(9); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b016632.txt", n, " ", d)); \\ Harry J. Smith, May 16 2009

Formula

log(9) = 2*Sum_{n >= 1} 1/(n*P(n, 5/4)*P(n-1, 5/4)), where P(n, x) denotes the n-th Legendre polynomial. The first 20 terms of the series gives the approximation log(9) = 2.19722457733(34...), correct to 11 decimal places. - Peter Bala, Mar 18 2024

Equals 2*A002391. - R. J. Mathar, Jun 10 2024