A016639 Decimal expansion of log(16) = 4*log(2).

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

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].

Peter Bala, A continued fraction expansion for the constant log(16)

Eric Weisstein's World of Mathematics, Madelung Constants.

Index entries for transcendental numbers

Formula

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).

Cf. A001008, A002805, A188859.

Sequence in context: A153738 A159790 A251809 * A138341 A153520 A153649

Adjacent sequences: A016636 A016637 A016638 * A016640 A016641 A016642

Keyword

nonn,cons

Author

N. J. A. Sloane

Status

approved