

A141803


Triangle read by rows derived from generalized ThueMorse sequences.


8



1, 1, 1, 1, 2, 0, 1, 2, 1, 1, 1, 2, 3, 2, 0, 1, 2, 3, 1, 0, 0, 1, 2, 3, 4, 2, 2, 1, 1, 2, 3, 4, 1, 3, 0, 1, 1, 2, 3, 4, 5, 2, 0, 1, 0, 1, 2, 3, 4, 5, 1, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 2, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 1, 3, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 2, 4, 2, 1, 2, 1, 1, 2, 3, 4, 5, 6, 7, 1, 3, 5, 3, 3, 0, 1
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OFFSET

1,5


COMMENTS

Triangle read by rows, antidiagonals of an array composed of generalized ThueMorse sequences [defined in A010060, comment of Zizka]. For each row of the array, n>0; nth term of mth row (m>0) = sum of digits of n in base (m+1), mod (m+1).
Every row of the array starting from the nth one as well as every row of the triangle starting from the (2*n1)th one begins from (1,2,3,...,n).
Row sums = A141804: (1, 2, 3, 5, 8, 7, 15, 15, 18, 22,...).
Row 1 of the array (corresponding to base 2) = A010060 (n>0), rows 2  8 are the sequences A053838  A053844, row 9 = A053837.


LINKS

Ivan Neretin, Table of n, a(n) for n = 1..8001


EXAMPLE

First few rows of the array are:
1, 1, 0, 1, 0, 0, 1, 1,...
1, 2, 1, 2, 0, 2, 0, 1,...
1, 2, 3, 1, 2, 3, 0, 2,...
1, 2, 3, 4, 1, 2, 3, 4,...
1, 2, 3, 4, 5, 1, 2, 3,...
1, 2, 3, 4, 5, 6, 1, 2,...
...
Triangle = antidiagonals of the array:
1;
1, 1;
1, 2, 0;
1, 2, 1, 1;
1, 2, 3, 2, 0;
1, 2, 3, 1, 0, 0;
1, 2, 3, 4, 2, 2, 1;
1, 2, 3, 4, 1, 3, 0, 1;
1, 2, 3, 4, 5, 2, 0, 1, 0;
1, 2, 3, 4, 5, 1, 3, 2, 1, 0;
1, 2, 3, 4, 5, 6, 2, 4, 3, 2, 1;
1, 2, 3, 4, 5, 6, 1, 3, 0, 0, 0, 0;
1, 2, 3, 4, 5, 6, 7, 2, 4, 2, 1, 2, 1;
1, 2, 3, 4, 5, 6, 7, 1, 3, 5, 3, 3, 0, 1;
...
a(8) = 2, = (3,2) of the array indicating that in the sequence 1,2,3,...mod 4, sum of digits of "2" mod 4 = 2.


MATHEMATICA

Flatten@Table[Mod[Total@IntegerDigits[n  i, i], i], {n, 16}, {i, n  1, 2, 1}] (* Ivan Neretin, Jun 18 2018 *)


CROSSREFS

Cf. A010060, A053837  A053844, A141804.
Sequence in context: A033793 A033785 A033781 * A249147 A260648 A127242
Adjacent sequences: A141800 A141801 A141802 * A141804 A141805 A141806


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson and Roger L. Bagula, Jul 06 2008


EXTENSIONS

Explanation in the Comments section corrected by Andrey Zabolotskiy, May 18 2016


STATUS

approved



