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%I #21 Mar 05 2017 11:01:39
%S 1,2,4,8,16,86,226,614,139,521,124,410,91,191,1111,332,97,257,919,
%T 1919,111118,33317,9997,272714,1111159,3331118,993316,2715713,1191796,
%U 31992512,719201242,15194288,77228248,21111212168,533544208,1391412416
%N Clone sequence C(2,3): a(1) = 1; for n > 1, a(n) is obtained by repeating each digit of a(n-1), summing the digits in groups of 3, and concatenating the digits of the sums.
%C The sequence of digital roots of a(n) has period 6: 1, 2, 4, 8, 7, 5.
%F a(n) = concat(s1,s2,s3,...) where sj is the sum of the j-th set of three digits in the "cloned" digit string obtained by repeating each digit of a(n-1).
%e a(9) is obtained from a(8) = 614 by cloning every digit of 614 to get 6,6,1,1,4,4, summing the digits three at a time to get (6+6+1, 1+4+4) = (13, 9), and concatenating the sums to get a(9) = 139.
%e a(1) = 1, so a(2) = 1 + 1 + 0 = 2;
%e a(5) = 16, so a(6) = concat(1 + 1 + 6, 6 + 0 + 0) = 86;
%e a(6) = 86, so a(7) = concat(8 + 8 + 6, 6 + 0 + 0) = 226;
%e a(7) = 226, so a(8) = concat(2 + 2 + 2, 2 + 6 + 6) = 614;
%e a(8) = 614, so a(9) = concat(6 + 6 + 1, 1 + 4 + 4) = 139.
%t NestList[FromDigits@ Flatten@ Map[IntegerDigits@ Total@ # &, Partition[PadRight[#, 3 Ceiling[Length@ #/3]], 3, 3]] &@ Riffle[#, #] &@ IntegerDigits@ # &, 1, 35] (* _Michael De Vlieger_, Mar 03 2017 *)
%K nonn,base,easy
%O 1,2
%A _Medjber Mohamed Mounir_, Mar 02 2017
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