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 A334025 #34 May 22 2020 18:05:19
%S A334025 0,1,2,24,448,48896,89697792,97792179395584,179395584195584358791168,
%T A334025 195584358791168358791168391168717582336,
%U A334025 358791168391168717582336391168717582336717582336782337435164672
%N A334025 a(0)=0, a(1)=1; and a(n) = {2*a(n-2), 2*a(n-1)}, where {x,y} is the concatenation of x and y.
%C A334025 This sequence, due to the process of concatenating one number with another, bears similarities to A131293 and other familiar sequences. However, unlike A131293, this sequence increases at a faster rate. It happens due to the multiplier applied to the existing terms, which increases the number of digits present in the successive term drastically (see a(7) and a(8)). a(11) is too large to include here and has 102 digits.
%e A334025 a(2) = {2*a(2-2), 2*a(2-1)} = {2*0, 2*1} = 02 = 2.
%e A334025 a(5) = {2*a(5-2), 2*a(5-1)} = {2*24, 2*448} = 48896.
%t A334025 a[0] = 0; a[1] = 1; a[n_] := a[n] = FromDigits @ Join[IntegerDigits[2*a[n - 2]], IntegerDigits[2*a[n - 1]]]; Array[a, 11, 0] (* _Amiram Eldar_, Apr 18 2020 *)
%Y A334025 Cf. A002605, A061107, A108047, A131293, A008352, A113526, A104458.
%K A334025 nonn,base
%O A334025 0,3
%A A334025 _Jamie Robert Creasey_, Apr 14 2020