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

1,3

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).

Links

Table of n, a(n) for n=1..60.

Example

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

Prog

(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

Crossrefs

Cf. A340407.

Sequence in context: A274211 A138499 A153387 * A010520 A169847 A285299

Adjacent sequences: A342258 A342259 A342260 * A342262 A342263 A342264

Keyword

nonn,tabf

Author

Thomas Scheuerle, Mar 26 2021

Status

approved