A357317 Inventory count sequence: record what you see and where it is located.

0, 1, 0, 0, 3, 0, 0, 2, 3, 1, 1, 1, 5, 0, 0, 2, 3, 5, 6, 4, 1, 1, 9, 10, 11, 1, 2, 7, 2, 3, 4, 8, 7, 0, 0, 2, 3, 5, 6, 13, 14, 7, 1, 1, 9, 10, 11, 20, 21, 25, 4, 2, 7, 15, 26, 28, 4, 3, 4, 8, 16, 29, 2, 4, 19, 30, 2, 5, 12, 17, 1, 6, 18, 1, 7, 27, 1, 8, 31, 1, 9, 22, 1, 10, 23, 1, 11, 24, 9, 0, 0, 2, 3

Offset

0,5

Comments

To get started we set a(0)=0. Now start with zero terms. We record ONE ZERO at position ZERO. The sequence is now 0,1,0,0. Now start again with zero terms. We record THREE ZEROS at positions 0,2,3. Next start with one terms. We record ONE ONE at position ONE. The sequence is now 0,1,0,0,3,0,0,2,3,1,1,1. Now start again with zero terms...one terms...two terms...three terms. The sequence is now 0,1,...,2,3,4,8. And so on.

Links

Thomas Scheuerle, Table of n, a(n) for n = 0..4895

Thomas Scheuerle, a(0..10000) as scatter plot

Example

a(0) = 0
counting over a(0):
a(1) = 1, a(2) = 0, a(3) = 0  (count one zero at position 0)
counting over a(0)..a(3):
a(4) = 3, a(5) = 0, a(6) = 0, a(7) = 2, a(8) = 3, (count 3 zeros at positions 0,2,3)
a(9) = 1, a(10) = 1, a(11) = 1 (count 1 one at position 1)
counting over a(0)..a(11):
a(12) = 5, a(13) = 0, a(14) = 0, a(15) = 2, a(16) = 3, a(17) = 5, a(18) = 6 (count 5 zeros at positions 0,2,3,5,6)
a(19) = 4, a(20) = 1, a(21) = 1, a(22) = 9, a(23) = 10, a(24) = 11 (count 4 ones at positions 1,9,10,11)
a(25) = 1, a(26) = 2, a(27) = 7 (count 1 two at position 7)
a(28) = 2, a(29) = 3, a(30) = 4, a(31) = 8 (count 2 threes at positions 4,8)
counting over a(0)..a(31):
etc.

Prog

(MATLAB)
function a = A357317( min_length )
    a = 0;
    while length(a) < min_length
        b = a; c = unique(a);
        for m = 1:length(c)
            nextnumber = c(m);
            indices = find(a == nextnumber);
            b = [b length(indices) nextnumber indices-1];
        end
        a = b;
    end
end % Thomas Scheuerle, Sep 29 2022

Crossrefs

Cf. A342585.

Sequence in context: A128113 A108930 A059682 * A357236 A156548 A112883

Adjacent sequences: A357314 A357315 A357316 * A357318 A357319 A357320

Keyword

nonn,look

Author

Ctibor O. Zizka, Sep 29 2022

Status

approved