A016632 - OEIS

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

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

OFFSET

1,1

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

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

EXAMPLE

2.197224577336219382790490473845051409294981115645498903469388667274988...

MATHEMATICA

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

PROG

(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

CROSSREFS

Cf. A016737 Continued fraction.

Sequence in context: A086572 A349035 A316606 * A176400 A021459 A133169

Adjacent sequences: A016629 A016630 A016631 * A016633 A016634 A016635

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane

STATUS

approved