cp's OEIS Frontend

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

%I A357317 #40 Oct 31 2022 06:00:26
%S A357317 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,
%T A357317 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,
%U A357317 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
%N A357317 Inventory count sequence: record what you see and where it is located.
%C A357317 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.
%H A357317 Thomas Scheuerle, <a href="/A357317/b357317.txt">Table of n, a(n) for n = 0..4895</a>
%H A357317 Thomas Scheuerle, <a href="/A357317/a357317.png">a(0..10000) as scatter plot</a>
%e A357317 a(0) = 0
%e A357317 counting over a(0):
%e A357317 a(1) = 1, a(2) = 0, a(3) = 0  (count one zero at position 0)
%e A357317 counting over a(0)..a(3):
%e A357317 a(4) = 3, a(5) = 0, a(6) = 0, a(7) = 2, a(8) = 3, (count 3 zeros at positions 0,2,3)
%e A357317 a(9) = 1, a(10) = 1, a(11) = 1 (count 1 one at position 1)
%e A357317 counting over a(0)..a(11):
%e A357317 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)
%e A357317 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)
%e A357317 a(25) = 1, a(26) = 2, a(27) = 7 (count 1 two at position 7)
%e A357317 a(28) = 2, a(29) = 3, a(30) = 4, a(31) = 8 (count 2 threes at positions 4,8)
%e A357317 counting over a(0)..a(31):
%e A357317 etc.
%o A357317 (MATLAB)
%o A357317 function a = A357317( min_length )
%o A357317     a = 0;
%o A357317     while length(a) < min_length
%o A357317         b = a; c = unique(a);
%o A357317         for m = 1:length(c)
%o A357317             nextnumber = c(m);
%o A357317             indices = find(a == nextnumber);
%o A357317             b = [b length(indices) nextnumber indices-1];
%o A357317         end
%o A357317         a = b;
%o A357317     end
%o A357317 end % _Thomas Scheuerle_, Sep 29 2022
%Y A357317 Cf. A342585.
%K A357317 nonn,look
%O A357317 0,5
%A A357317 _Ctibor O. Zizka_, Sep 29 2022