Search: id:A141803
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%I A141803
%S A141803 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,
%T A141803 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,
%U A141803 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
%N A141803 Triangle read by rows derived from generalized Thue-Morse sequences.
%C A141803 Rows converge to (1,2,3,...).
%C A141803 Row sums = A141804: (1, 2, 3, 5, 8, 7, 15, 15, 18, 22,...).
%C A141803 Row 2 of the array = A010060 (n>0), row 3 = A053838, row 4 = A053839, 
               row 5 = A053840, row 6 = A053841.
%F A141803 Triangle read by rows, antidiagonals of an array composed of generalized 
               Thue-Morse sequences [defined in A010060, comment of Zizka]. For 
               each row, n>0; n-th term = sum of digits of n in base n, mod n.
%e A141803 First few rows of the array are (rows, n>1 since the Morse-Thue sequence 
               starting with "1" = A010060 = (1, 1, 0, 1, 0, 0, 1, 1, 0,...).
%e A141803 1, 1, 0, 1, 0, 0, 1, 1,...
%e A141803 1, 2, 1, 2, 0, 2, 0, 1,...
%e A141803 1, 2, 3, 1, 2, 3, 0, 2,...
%e A141803 1, 2, 3, 4, 1, 2, 3, 4,...
%e A141803 1, 2, 3, 4, 5, 1, 2, 3,...
%e A141803 1, 2, 3, 4, 5, 6, 1, 2,...
%e A141803 ...
%e A141803 Triangle = antidiagonals of the array:
%e A141803 1;
%e A141803 1, 1;
%e A141803 1, 2, 0;
%e A141803 1, 2, 1, 1;
%e A141803 1, 2, 3, 2, 0;
%e A141803 1, 2, 3, 1, 0, 0;
%e A141803 1, 2, 3, 4, 2, 2, 1;
%e A141803 1, 2, 3, 4, 1, 3, 0, 1;
%e A141803 1, 2, 3, 4, 5, 2, 0, 1, 0;
%e A141803 1, 2, 3, 4, 5, 1, 3, 2, 1, 0;
%e A141803 1, 2, 3, 4, 5, 6, 2, 4, 3, 2, 1;
%e A141803 1, 2, 3, 4, 5, 6, 1, 3, 0, 0, 0, 0;
%e A141803 1, 2, 3, 4, 5, 6, 7, 2, 4, 2, 1, 2, 1;
%e A141803 1, 2, 3, 4, 5, 6, 7, 1, 3, 5, 3, 3, 0, 1;
%e A141803 ...
%e A141803 a(8) = 2, = (4,2) of the array indicating that in the sequence 1,2,3,
               ...mod 4, sum of digits of "2" mod 4 = 2.
%Y A141803 Cf. A010060, A053838, A053839, A053840, A053841, A141804.
%Y A141803 Sequence in context: A033793 A033785 A033781 this_sequence A127242 A025853 
               A025847
%Y A141803 Adjacent sequences: A141800 A141801 A141802 this_sequence A141804 A141805 
               A141806
%K A141803 nonn,tabl
%O A141803 1,5
%A A141803 Gary W. Adamson & Roger L. Bagula (qntmpkt(AT)yahoo.com), Jul 06 2008

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