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A002285 Decimal expansion of common logarithm of e.
(Formerly M3210 N1299)
10
4, 3, 4, 2, 9, 4, 4, 8, 1, 9, 0, 3, 2, 5, 1, 8, 2, 7, 6, 5, 1, 1, 2, 8, 9, 1, 8, 9, 1, 6, 6, 0, 5, 0, 8, 2, 2, 9, 4, 3, 9, 7, 0, 0, 5, 8, 0, 3, 6, 6, 6, 5, 6, 6, 1, 1, 4, 4, 5, 3, 7, 8, 3, 1, 6, 5, 8, 6, 4, 6, 4, 9, 2, 0, 8, 8, 7, 0, 7, 7, 4, 7, 2, 9, 2, 2, 4, 9, 4, 9, 3, 3, 8, 4, 3, 1, 7, 4, 8, 3, 1, 8, 7, 0, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Sometimes also called Briggs's constant after the English mathematician Henry Briggs (1561-1630). - Martin Renner, Jan 03 2022
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.
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).
LINKS
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].
J. Sondow and E. W. Weisstein, MathWorld: Harmonic Number
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.
Wikipedia, Henry Briggs
FORMULA
Equals log_10(e) = 1/log(10) = 1/A002392. - Eric Desbiaux, Jun 27 2009
Conjecture by Eric Weisstein: Equals lim_{n->oo} b(n)/10^(n-1), for b=A114467 or b=A114468 (i.e., is the limit of the decimal expansion of the number of decimal digits in both the numerator and denominator of the (10^n)th harmonic number). More generally, log_k(e) seems to equal lim_{n->oo} floor(log_k(b(k^n)))/k^(n-1), for b=A001008 or b=A002805 and k >= 2. - Nathan L. Skirrow, Feb 12 2023
EXAMPLE
0.4342944819...
MAPLE
evalf[100](1/log(10)); # Martin Renner, Jan 03 2022
MATHEMATICA
RealDigits[N[1/Log[10], 100]][[1]] (* Vincenzo Librandi, Mar 25 2013 *)
RealDigits[Log10[E], 10, 120][[1]] (* Harvey P. Dale, Apr 17 2022 *)
PROG
(PARI) 1/log(10) \\ Charles R Greathouse IV, Jan 04 2016
CROSSREFS
Sequence in context: A082125 A058290 A356033 * A106049 A367914 A238234
KEYWORD
nonn,cons
AUTHOR
STATUS
approved

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Last modified March 19 01:57 EDT 2024. Contains 370952 sequences. (Running on oeis4.)