A016629 Decimal expansion of log(6).
1, 7, 9, 1, 7, 5, 9, 4, 6, 9, 2, 2, 8, 0, 5, 5, 0, 0, 0, 8, 1, 2, 4, 7, 7, 3, 5, 8, 3, 8, 0, 7, 0, 2, 2, 7, 2, 7, 2, 2, 9, 9, 0, 6, 9, 2, 1, 8, 3, 0, 0, 4, 7, 0, 5, 8, 5, 5, 3, 7, 4, 3, 4, 3, 1, 3, 0, 8, 8, 7, 9, 1, 5, 1, 8, 8, 3, 0, 3, 6, 8, 2, 4, 7, 9, 4, 7, 9, 0, 8, 1, 8, 1, 0, 1, 5, 0, 7, 7
Offset: 1
Examples
1.791759469228055000812477358380702272722990692183004705855374343130887...
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].
- Matt Parker, What's the story with log(1 + 2 + 3)?, standupmaths video (2019)
- Index entries for transcendental numbers
Crossrefs
Cf. A016734 (continued fraction).
Programs
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Mathematica
First[RealDigits[Log[6], 10, 100]] (* Paolo Xausa, Mar 21 2024 *)
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PARI
default(realprecision, 20080); x=log(6); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b016629.txt", n, " ", d)); \\ Harry J. Smith, May 16 2009
Formula
log(6) = 2*Sum_{n >= 1} 1/(n*P(n, 7/5)*P(n-1, 7/5)), where P(n, x) denotes the n-th Legendre polynomial. The first 20 terms of the series gives the approximation log(6) = 1.79175946922805(27...), correct to 14 decimal places. - Peter Bala, Mar 19 2024