This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A384683 #28 Jun 13 2025 00:12:44
%S A384683 2,4,7,0,0,6,2,5,0,2,9,5,0,1,8,5,3,7,2,6,5,2,7,6,2,4,2,1,8,7,5,7,0,2,
%T A384683 3,0,2,7,6,4,0,0,9,0,4,2,2,9,2,5,1,2,9,6,6,0,5,6,9,9,6,7,7,5,8,7,3,9,
%U A384683 3,2,8,3,0,8,8,2,4,5,5,0,2,8,2,2,7,8,7,0,4,6,0,3,8,1,8,9,3,4,9,5,8,4,6,1,4,6,1,2,1,1,9,4,6,7,8,4
%N A384683 Decimal expansion of Sum_{i >= 1} 1/(3*i-1) - 1/(3*i).
%C A384683 Generalization of infinite sum generating A002162 (natural logarithm of 2). That sum is Sum_{i >= 1} 1/(k*i-1) - 1/(k*i), where k = 2. Here, we set k = 3.
%H A384683 Jason Bard, <a href="/A384683/b384683.txt">Table of n, a(n) for n = 0..9999</a>
%H A384683 Michael I. Shamos, <a href="http://euro.ecom.cmu.edu/people/faculty/mshamos/cat.pdf">A catalog of the real numbers</a>, (2007). See p. 291.
%H A384683 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A384683 Equals (1/2) * log(3) - sqrt(3) * Pi / 18.
%F A384683 Equals Sum_{i>=1} 1/A152743(i).
%F A384683 Equals A294514/3. - _Hugo Pfoertner_, Jun 07 2025
%e A384683 0.24700625029501853726527624218757023027640090422925...
%t A384683 RealDigits[1/2 * Log[3] - (Sqrt[3]/18) * Pi, 10, 1000][[1]]
%o A384683 (PARI) log(3)/2 - Pi/(6*sqrt(3)) \\ _Amiram Eldar_, Jun 07 2025
%Y A384683 Cf. A002162, A007494, A152743, A156057, A294514, A381671.
%K A384683 nonn,cons
%O A384683 0,1
%A A384683 _Jason Bard_, Jun 06 2025