A328096 a(0) = 0; a(1) = 1; for n > 1, a(n) = number of terms between the two previous occurrences of a(n-1) if a(n-1) has appeared two or more times, otherwise a(n) = 0.

0, 1, 0, 1, 1, 0, 2, 0, 1, 3, 0, 2, 4, 0, 2, 2, 0, 2, 1, 9, 0, 3, 11, 0, 2, 6, 0, 2, 2, 0, 2, 1, 12, 0, 3, 12, 2, 5, 0, 4, 26, 0, 2, 5, 5, 0, 3, 11, 24, 0, 3, 3, 0, 2, 10, 0, 2, 2, 0, 2, 1, 28, 0, 3, 11, 16, 0, 3, 3, 0, 2, 10, 16, 6, 47, 0, 5, 31, 0, 2, 8

Offset: 0

Author

Scott R. Shannon, Oct 04 2019

Keywords

• nonn

Comments

In the first 10000 terms the largest entry is 9040, which is the number of terms between the two appearances of 217. The longest run of nonzero values is 19, starting at a(9740) = 3 and ending at a(9758) = 6400. The smallest number not appearing is 258.

Examples

			a(3) = 1 as there is 1 term between a(3-1) = a(2) = 0 and a(0) = 0.
a(5) = 0 as there are no terms between a(5-1) = a(4) = 1 and a(3) = 1.
a(7) = 0 as a(7-1) = a(6) = 2 has only appeared once up to n = 7.
a(12) = 4 as there are 4 terms between a(12-1) = a(11) = 2 and a(6) = 2.
a(22) = 11 as there are 11 terms between a(22-1) = a(21) = 3 and a(9) = 3.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A181391, A309261.

Programs

Maple

a:= proc(n) option remember; local t, j;
      if n<2 then n else t:= a(n-1);
        for j from 2 to n do
          if a(n-j)=t then return j-2 fi
        od; 0
      fi
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Oct 04 2019

Mathematica

a = {0,1}; While[Length@a < 90, p = Flatten@ Position[Reverse@ a, Last@a, 1, 2]; AppendTo[a, If[ Length@p == 1, 0, p[[2]] - p[[1]] - 1]]]; a (* Giovanni Resta, Oct 04 2019 *)