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%I #34 May 22 2020 18:05:19
%S 0,1,2,24,448,48896,89697792,97792179395584,179395584195584358791168,
%T 195584358791168358791168391168717582336,
%U 358791168391168717582336391168717582336717582336782337435164672
%N 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 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 a(2) = {2*a(2-2), 2*a(2-1)} = {2*0, 2*1} = 02 = 2.
%e a(5) = {2*a(5-2), 2*a(5-1)} = {2*24, 2*448} = 48896.
%t 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 Cf. A002605, A061107, A108047, A131293, A008352, A113526, A104458.
%K nonn,base
%O 0,3
%A _Jamie Robert Creasey_, Apr 14 2020
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