1,5

Rows converge to (1,2,3,...).

Row sums = A141804: (1, 2, 3, 5, 8, 7, 15, 15, 18, 22,...).

Row 2 of the array = A010060 (n>0), row 3 = A053838, row 4 = A053839, row 5 = A053840, row 6 = A053841.

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.

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,...).

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, = (4,2) of the array indicating that in the sequence 1,2,3,...mod 4, sum of digits of "2" mod 4 = 2.

Cf. A010060, A053838, A053839, A053840, A053841, A141804.

Sequence in context: A033793 A033785 A033781 this_sequence A127242 A025853 A025847

Adjacent sequences: A141800 A141801 A141802 this_sequence A141804 A141805 A141806

nonn,tabl

Gary W. Adamson & Roger L. Bagula (qntmpkt(AT)yahoo.com), Jul 06 2008