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 A215713 #21 Sep 08 2022 08:46:03
%S A215713 4,8,64,16,1024,2048,16384,16384,262144,524288,4194304,2097152,
%T A215713 67108864,134217728,1073741824,1073741824,17179869184,34359738368,
%U A215713 274877906944,17179869184,4398046511104,8796093022208,70368744177664,70368744177664,1125899906842624
%N A215713 Denominator of sum(i=1..n, 3*i/4^i).
%C A215713 The odd-indexed terms are the even-indexed powers of 4 (A013709).
%D A215713 Calvin C. Clawson, The Beauty and Magic of Numbers. New York: Plenum Press (1996): 96.
%H A215713 Colin Barker, <a href="/A215713/b215713.txt">Table of n, a(n) for n = 1..1000</a>
%e A215713 a(4) = 16 because 3/4 + 6/16 + 9/64 + 12/256 = 3/4 + 3/8 + 9/64 + 3/64 = 48/64 + 24/64 + 9/64 + 3/64 = 84/64 = 21/16.
%t A215713 Table[Denominator[Sum[3i/4^i, {i, n}]], {n, 40}]
%o A215713 (Magma) [Denominator(&+[3*i/4^i: i in [1..n]]): n in [1..25]]; // _Bruno Berselli_, Sep 03 2012
%o A215713 (PARI) vector(100, n, denominator(sum(i=1, n, 3*i/4^i))) \\ _Colin Barker_, Nov 09 2014
%Y A215713 Cf. A215712 for the numerators. A036295/A036296 is very similar but with i/2^i instead of 3i/4^i. Cf. also A122553.
%K A215713 nonn,easy,frac
%O A215713 1,1
%A A215713 _Alonso del Arte_, Aug 21 2012