A283195 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.

1, 2, 4, 8, 16, 86, 226, 614, 139, 521, 124, 410, 91, 191, 1111, 332, 97, 257, 919, 1919, 111118, 33317, 9997, 272714, 1111159, 3331118, 993316, 2715713, 1191796, 31992512, 719201242, 15194288, 77228248, 21111212168, 533544208, 1391412416

Offset

1,2

Comments

The sequence of digital roots of a(n) has period 6: 1, 2, 4, 8, 7, 5.

Links

Table of n, a(n) for n=1..36.

Formula

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).

Example

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.
a(1) = 1, so a(2) = 1 + 1 + 0 = 2;
a(5) = 16, so a(6) = concat(1 + 1 + 6, 6 + 0 + 0) = 86;
a(6) = 86, so a(7) = concat(8 + 8 + 6, 6 + 0 + 0) = 226;
a(7) = 226, so a(8) = concat(2 + 2 + 2, 2 + 6 + 6) = 614;
a(8) = 614, so a(9) = concat(6 + 6 + 1, 1 + 4 + 4) = 139.

Mathematica

NestList[FromDigits@ Flatten@ Map[IntegerDigits@ Total@ # &, Partition[PadRight[#, 3 Ceiling[Length@ #/3]], 3, 3]] &@ Riffle[#, #] &@ IntegerDigits@ # &, 1, 35] (* Michael De Vlieger, Mar 03 2017 *)

Crossrefs

Sequence in context: A097049 A119490 A013174 * A233294 A287706 A287705

Adjacent sequences: A283192 A283193 A283194 * A283196 A283197 A283198

Keyword

nonn,base,easy

Author

Medjber Mohamed Mounir, Mar 02 2017

Status

approved