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A357317
Inventory count sequence: record what you see and where it is located.
5
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
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
KEYWORD
nonn,look
AUTHOR
Ctibor O. Zizka, Sep 29 2022
STATUS
approved