A342261 Irregular triangular array T(n,k) = m read by rows. Row n lists all solutions m < 3^n, where A340407(3^n*j - m) = n is true for all j > 0, sorted in ascending order.

0, 1, 8, 2, 4, 5, 16, 13, 14, 22, 34, 38, 52, 74, 77, 20, 25, 40, 50, 88, 130, 146, 173, 185, 203, 209, 223, 229, 230, 238, 241, 130, 146, 173, 185, 203, 209, 223, 229, 230, 238, 241, 41, 61, 76, 104, 106, 121, 128, 157, 254, 266, 292, 311, 403, 412, 430, 445, 454, 493

Offset: 1

Author

Thomas Scheuerle, Mar 26 2021

Keywords

• nonn
• tabf

Comments

Each row n has 2^(n-1) values.

In all rows other than the first row of T(n,k), there are exactly 2^(n-2) numbers of the form 3*p + 1 and the same number of numbers of the form 3*q - 1.

Each integer has a unique representation of the form 3^n*j - T(n,k).

Examples

			Triangle T(n,k) begins:
  0;
  1,   8;
  2,   4,  5, 16;
  13, 14, 22, 34, 38, 52, 74, 77;
		

Crossrefs

Cf. A340407.

Programs

MATLAB

function t = A342261 (max_row)
    maxtest = 10;
    d = A340407(maxtest*3^max_row);
    for row = 1:max_row
        m = 0;
        for k = 1:2^(row-1)
            test = d((1:maxtest)*(3^row)-m);
            while ~all(test == test(1))||(test(1) ~= row)
                m = m+1;
                test = d((1:maxtest)*(3^row)-m);
            end
            t(row,k) = m;
            t = t+1;
        end
    end
end
function d = A340407 (max_p)
    for p = 1:max_p
        s = 6*p -2;
        c = 0;
        while mod(s,3) ~= 0
            s = A342369( s );
           if mod(s,3) == 2
                c = c+1;
            end
        end
        d(p) = c;
    end
end
function b = A342369( n )
    if mod(n,3) == 2
        b = (2*n - 1)/3;
    else
        b = 2*n;
    end
end