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

1,4

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.

Links

Table of n, a(n) for n=1..100.

Prog

(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

Crossrefs

Cf. A181391.

Sequence in context: A061199 A352128 A334203 * A366353 A366354 A144741

Adjacent sequences: A309104 A309105 A309106 * A309108 A309109 A309110

Keyword

easy,nonn

Author

Christian Schroeder, Jul 12 2019

Status

approved