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

0,7

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.

Links

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

Example

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.

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 *)

Crossrefs

Cf. A181391, A309261.

Sequence in context: A022880 A366614 A128097 * A353778 A173662 A263406

Adjacent sequences: A328093 A328094 A328095 * A328097 A328098 A328099

Keyword

nonn

Author

Scott R. Shannon, Oct 04 2019

Status

approved