A309107 A member of a family of generalizations of van Eck's sequence as defined below.

0, 0, 0, 2, 0, 2, 2, 3, 0, 4, 0, 2, 5, 0, 3, 7, 0, 3, 3, 4, 10, 0, 5, 10, 3, 6, 0, 5, 5, 6, 4, 11, 0, 6, 4, 4, 5, 8, 0, 6, 6, 7, 26, 0, 5, 8, 8, 9, 0, 5, 5, 6, 11, 21, 0, 6, 4, 21, 4, 2, 48, 0, 7, 21, 6, 9, 18, 0, 6, 4, 11, 18, 5, 22, 0, 7, 13, 0, 3, 54, 0, 3, 3, 4, 14, 0, 5, 14, 3, 6, 21, 27, 0, 7, 18, 23, 0, 4, 14, 11

Offset: 1

Author

Christian Schroeder, Jul 12 2019

Keywords

• easy
• nonn

Comments

For n >= 1, if there exists an m < n-1 such that a(m) = a(n), take the largest such m and set a(n+1) = n-m; otherwise a(n+1) = 0. Start with a(1) = a(2) = 0.

T: let 0 <= k < l. For n > k, if there exists an m <= n-l such that a(m) = a(n-k), take the largest such m and set a(n+1) = n-m; otherwise a(n+1) = 0. Start with a(1) = ... = a(l) = 0. Setting k = 0, l = 1 produces van Eck's sequence A181391; setting k = 0, l = 2 produces this sequence.

Crossrefs

Cf. A181391.

Programs

MATLAB

function VEg = VE_generalized(N, k, l)
    assert(l > k);
    VEg = zeros(1, l);
    for n = l:(N - 1)
        prev = VEg(n - k);
        VEg(n + 1) = 0;
        for j = (n - l):-1:1
            if VEg(j) == prev
                VEg(n + 1) = n - j;
                break
            end
        end
    end
end