A340351 Square array, read by descending antidiagonals, where row n gives all solutions k > 0 to A000120(k)=A000120(k*n), A000120 is the Hamming weight.

1, 2, 1, 3, 2, 3, 4, 3, 6, 1, 5, 4, 7, 2, 7, 6, 5, 12, 3, 14, 3, 7, 6, 14, 4, 15, 6, 7, 8, 7, 15, 5, 27, 7, 14, 1, 9, 8, 24, 6, 28, 12, 15, 2, 15, 10, 9, 28, 7, 30, 14, 19, 3, 30, 7, 11, 10, 30, 8, 31, 15, 28, 4, 31, 14, 3, 12, 11, 31, 9, 39, 24, 30, 5, 43, 15, 6, 3, 13, 12

Offset: 1

Author

Thomas Scheuerle, Jan 05 2021

Keywords

• nonn
• base
• tabl

Comments

Square array is read by descending antidiagonals, as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

Rows at positions 2^k are 1, 2, 3, ..., (A000027). Row 2n is equal to row n.

Values are different from those in A115872, because we use multiplication with carry here.

Examples

			Eight initial terms of rows 1 - 8 are listed below:
   1:  1,  2,  3,   4,   5,   6,   7,   8, ...
   2:  1,  2,  3,   4,   5,   6,   7,   8, ...
   3:  3,  6,  7,  12,  14,  15,  24,  28, ...
   4:  1,  2,  3,   4,   5,   6,   7,   8, ...
   5:  7, 14, 15,  27,  28,  30,  31,  39, ...
   6:  3,  6,  7,  12,  14,  15,  24,  28, ...
   7:  7, 14, 15,  19,  28,  30,  31,  37, ...
   8:  1,  2,  3,   4,   5,   6,   7,   8, ...
a(6,3) = 7 because: 7 in binary is 111 and 6*7 = 42 in binary is 101001, both have 3 bits set to 1.
		

Crossrefs

Cf. A000120, A292849 (1st column), A340069, A077459 (3rd row).

Programs

MATLAB

function [a] = A340351(max_n)
    for n = 1:max_n
        m = 1;
        k = 1;
        while m < max_n
            c = length(find(bitget(k,1:32)== 1));
            if c == length(find(bitget(n*k,1:32)== 1))
                a(n,m) = k;
                m = m+1;
            end
            k = k +1;
        end
    end
end