A002392 Decimal expansion of natural logarithm of 10.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• cons
• nonn

Examples

			2.302585092994045684017991454684364207601101488628772976033327900967572...
		

References

• John H. Conway and Richard K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996. See pp. 24, 143.
• W. E. Mansell, Tables of Natural and Common Logarithms. Royal Society Mathematical Tables, Vol. 8, Cambridge Univ. Press, 1964, p. 2.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
• Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 25, pages 227, 232.
• David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 45.

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• Bakir Farhi, A curious result related to Kempner's series, arXiv:0807.3518 [math.NT], Jul 22 2008.
• A. J. Kempner, A curious convergent series, Amer. Math. Monthly 23 (1914) pp. 48-50.
• Simon Plouffe, log(10) the natural logarithm of 10 to 2000 digits.
• Simon Plouffe, Plouffe's Inverter, The natural logarithm of 10 to 2000 digits.
• Horace S. Uhler, Recalculation and extension of the modulus and of the logarithms of 2, 3, 5, 7 and 17, Proc. Nat. Acad. Sci. U. S. A. 26, (1940) pp. 205-212.
• Eric Weisstein's World of Mathematics, Natural Logarithm of 10.
• Index entries for transcendental numbers.

Crossrefs

Cf. A016738 (continued fraction).

Programs

Mathematica

RealDigits[Log[10],10,120][[1]] (* Harvey P. Dale, Nov 23 2013 *)

PARI

default(realprecision, 20080); x=log(10); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b002392.txt", n, " ", d)); \\ Harry J. Smith, Apr 16 2009

Formula

Equals A002162 + A016628. - R. J. Mathar, Jul 22 2025