# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a016639 Showing 1-1 of 1 %I A016639 #58 Jun 10 2024 07:13:35 %S A016639 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, %T A016639 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, %U A016639 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 %N A016639 Decimal expansion of log(16) = 4*log(2). %D A016639 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. %H A016639 Harry J. Smith, Table of n, a(n) for n = 1..20000 %H A016639 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]. %H A016639 Peter Bala, A continued fraction expansion for the constant log(16) %H A016639 Eric Weisstein's World of Mathematics, Madelung Constants. %H A016639 Index entries for transcendental numbers %F A016639 Equals 4*A002162. %F A016639 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 %F A016639 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 %F A016639 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 %F A016639 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 %e A016639 2.77258872223978123766892848583270627230200053744102101648272... - _Harry J. Smith_, May 17 2009 %t A016639 RealDigits[Log[16], 10, 120][[1]] (* _Harvey P. Dale_, Jun 12 2012 *) %o A016639 (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 %o A016639 (Magma) Log(16); // _Vincenzo Librandi_, Feb 20 2015 %Y A016639 Equals 4*A002162. %Y A016639 Equals (4/5)*A016655. %Y A016639 Equals A303658 + 2. %Y A016639 Cf. A016444 (continued fraction). %Y A016639 Cf. A001008, A002805, A188859. %K A016639 nonn,cons %O A016639 1,1 %A A016639 _N. J. A. Sloane_ # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE