login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A016639
Decimal expansion of log(16) = 4*log(2).
9
2, 7, 7, 2, 5, 8, 8, 7, 2, 2, 2, 3, 9, 7, 8, 1, 2, 3, 7, 6, 6, 8, 9, 2, 8, 4, 8, 5, 8, 3, 2, 7, 0, 6, 2, 7, 2, 3, 0, 2, 0, 0, 0, 5, 3, 7, 4, 4, 1, 0, 2, 1, 0, 1, 6, 4, 8, 2, 7, 2, 0, 0, 3, 7, 9, 7, 3, 5, 7, 4, 4, 8, 7, 8, 7, 8, 7, 7, 8, 8, 6, 2, 4, 2, 3, 4, 5, 3, 3, 0, 7, 9, 8, 5, 6, 7, 4, 7, 5
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
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].
Eric Weisstein's World of Mathematics, Madelung Constants.
FORMULA
Equals 4*A002162.
Equals Sum_{k=1..4} (-1)^(k+1) gamma(0, k/4) where gamma(n,x) denotes the generalized Stieltjes constants. - Peter Luschny, May 16 2018
Equals -2 + Sum_{k>=1} H(k)*(k+1)/2^k, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number. - Amiram Eldar, May 28 2021
Equals 1 + Limit_{n -> infinity} (1/n)*Sum_{k = 1..n} (2*n + k)/(2*n - k) = 2*( 1 + Limit_{n -> infinity} (1/n)*Sum_{k = 1..n} (n - k)/(n + k) ). - Peter Bala, Oct 10 2021
Equals 2 + 1/(1 + 1/(3 + 2/(4 + 6/(5 + 6/(6 + 12/(7 + 12/(8 + ... + n*(n-1)/(2*n-1 + n*(n-1)/(2*n + ...))))))))). Cf. A188859. - Peter Bala, Mar 04 2024
EXAMPLE
2.77258872223978123766892848583270627230200053744102101648272... - Harry J. Smith, May 17 2009
MATHEMATICA
RealDigits[Log[16], 10, 120][[1]] (* Harvey P. Dale, Jun 12 2012 *)
PROG
(PARI) default(realprecision, 20080); x=log(16); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b016639.txt", n, " ", d)); \\ Harry J. Smith, May 17 2009, corrected May 19 2009
(Magma) Log(16); // Vincenzo Librandi, Feb 20 2015
CROSSREFS
Equals 4*A002162.
Equals (4/5)*A016655.
Equals A303658 + 2.
Cf. A016444 (continued fraction).
Sequence in context: A153738 A159790 A251809 * A138341 A374525 A374526
KEYWORD
nonn,cons
STATUS
approved