

A328096


a(0) = 0; a(1) = 1; for n > 1, a(n) = number of terms between the two previous occurrences of a(n1) if a(n1) has appeared two or more times, otherwise a(n) = 0.


3



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
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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



EXAMPLE

a(3) = 1 as there is 1 term between a(31) = a(2) = 0 and a(0) = 0.
a(5) = 0 as there are no terms between a(51) = a(4) = 1 and a(3) = 1.
a(7) = 0 as a(71) = a(6) = 2 has only appeared once up to n = 7.
a(12) = 4 as there are 4 terms between a(121) = a(11) = 2 and a(6) = 2.
a(22) = 11 as there are 11 terms between a(221) = a(21) = 3 and a(9) = 3.


MAPLE

a:= proc(n) option remember; local t, j;
if n<2 then n else t:= a(n1);
for j from 2 to n do
if a(nj)=t then return j2 fi
od; 0
fi
end:


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



KEYWORD

nonn


AUTHOR



STATUS

approved



