cp's OEIS Frontend

A347062 Record the number of zero terms having a following term, then the number of terms equal to 1 having a following term, then 2, 3, etc. until recording a zero, whereupon the count is reset.

%I A347062 #57 Nov 22 2021 13:30:21
%S A347062 0,0,1,0,2,1,1,0,3,3,1,2,0,4,4,2,2,2,0,5,4,5,2,3,2,0,6,4,7,3,4,2,1,1,
%T A347062 0,7,6,8,4,5,2,2,2,1,0,8,7,11,4,6,3,3,3,2,0,9,7,12,7,7,3,3,6,2,1,0,10,
%U A347062 8,13,9,7,3,4,7,3,2,1,1,1,1,0,11,12,14,11,8
%N A347062 Record the number of zero terms having a following term, then the number of terms equal to 1 having a following term, then 2, 3, etc. until recording a zero, whereupon the count is reset.
%C A347062 Inventory sequence recording the number of existing terms immediately following occurrences of a zero term, then the number immediately following occurrences of 1, then 2, and so on until another zero is recorded, after which the count is reset. Inclusion of a term in any count requires it to have been followed by another term first, therefore lead terms are not included in the current count.
%C A347062 The scatterplot exhibits trajectories attributable to the register of occurrences of the immediately-preceding term m, c(m), and irregular periodicity of nondecreasing length. - _Michael De Vlieger_, Oct 16 2021
%C A347062 Suggested by A342585.
%H A347062 Michael De Vlieger, <a href="/A347062/a347062.png">Scatterplot of a(n)</a> for n=0..2877 (rows 0..31)
%H A347062 Michael De Vlieger, <a href="/A347062/a347062_1.png">Labeled scatterplot of a(n)</a> for n=0..336 (rows 0..23), with trajectory of c(0) in black, c(1) in red, c(2) in orange, c(3) in yellow, c(4) in green, c(5) in blue, and c(6) in purple.
%H A347062 Michael De Vlieger, <a href="/A347062/a347062_2.png">Scatterplot of a(n)</a> for n=0..39555 (rows 0..255), showing trajectories with color function as stated above.
%e A347062 At first there are no terms, thus none following a zero, so a(0) = 0.
%e A347062 After a(0) = 0 the count is reset, and since there are still no terms following a zero, a(1) = 0. The count is now reset again and we have one term a(1) = 0 which follows a zero term, so a(2) = 1.
%e A347062 We now have 0,0,1 and because no term yet follows 1, a(3) must be 0 (the lead term here is 1 but it is not counted).
%e A347062 The count is now reset and there are two terms (a(1) and a(2)) which follow a zero term, thus a(4) = 2; etc.
%e A347062 As an irregular triangle the sequence begins:
%e A347062 0;
%e A347062 0;
%e A347062 1, 0;
%e A347062 2, 1, 1, 0;
%e A347062 3, 3, 1, 2, 0;
%e A347062 4, 4, 2, 2, 2, 0;
%e A347062 5, 4, 5, 2, 3, 2, 0;
%e A347062 6, 4, 7, 3, 4, 2, 1, 1, 0;
%e A347062 ...
%t A347062 Block[{c, k, m, n}, c[0] = 1; m = 0; {0, 0}~Join~Reap[Do[k = 0; While[IntegerQ[c[k]], Set[n, c[k]]; Sow[n]; If[IntegerQ@ c[m], c[m]++, c[m] = 1]; Set[m, n]; k++]; Sow[0]; If[IntegerQ@ c[m], c[m]++, c[m] = 1]; Set[m, 0], 11]][[-1, -1]]] (* _Michael De Vlieger_, Oct 16 2021 *)
%Y A347062 Cf. A342585, A347564.
%K A347062 nonn,tabf
%O A347062 0,5
%A A347062 _David James Sycamore_, Oct 16 2021