

A309035


If a(n) is not a term of a(0),...,a(n1), then a(n+1) = n  m, where m is the most recent time that some new value a(m) appeared for the first time; otherwise a(n+1) is the number of terms equal to a(n) in a(0),...,a(n1). Start with a(0)=0, a(1)=0.


2



0, 0, 1, 2, 1, 1, 2, 1, 3, 5, 1, 4, 2, 2, 3, 1, 5, 1, 6, 7, 1, 7, 1, 8, 4, 1, 9, 3, 2, 4, 2, 5, 2, 6, 1, 10, 9, 1, 11, 3, 3, 4, 3, 5, 3, 6, 2, 7, 2, 8, 1, 12, 13, 1, 13, 1, 14, 4, 4, 5, 4, 6, 3, 7, 3, 8, 2, 9, 2, 10, 1, 15, 15, 1, 16, 3, 9, 3, 10, 2, 11, 1, 17, 8, 3, 11, 2, 12, 1, 18, 7, 4, 7, 5, 5, 6, 4, 8, 4, 9, 4
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OFFSET

0,4


COMMENTS

In other words, if the last term a(n) has not appeared previously, take the difference between its index n and the lowest index m of the last term to appear for the first time to obtain the next term. Otherwise, the next term is the number of terms equal to a(n) in a(0),...,a(n1).


LINKS

Table of n, a(n) for n=0..100.


EXAMPLE

a(0)=0 (given).
a(1)=0 (given).
a(2)=1: a(1)=0 is a term of a(0..0), therefore a(2) = number of terms=0 in a(0..0) = 1.
a(3)=2: a(2)=1 is not a term of a(0..1), first appearance of a new term is at a(0), therefore a(3) = 2  0 = 2.
a(4)=1: a(3)=2 is not a term of a(0..2), first appearance of a new term is at a(2), therefore: 3  2 = 1.
a(5)=1: a(4)=1 is a term of a(0..3), therefore a(5) = Number of terms=1 in a(0..3) = 1.
a(6)=2: a(5)=1 is a term of a(0..4), therefore a(6) = Number of terms=1 in a(0..4) = 2.
a(7)=1: a(6)=2 is a term of a(0..5), therefore a(7) = Number of terms=2 in a(0..5) = 1.
a(8)=3: a(7)=1 is a term of a(0..6), therefore a(8) = Number of terms=1 in a(0..6) = 3.
a(9)=5: a(8)=3 is not a term of a(0..7), first appearance of a new term is at a(3), therefore: 8  3 = 5.
a(10)=1: a(9)=5 is not a term of a(0..8), first appearance of a new term is at a(8), therefore: 9  8 = 1.


PROG

(PARI) lista(NN) = {v = vector(NN); m=0; v[1]=0; v[2]=1; for(k=2, NN1, v[k+1]=sum(j=1, k1, v[j]==v[k]); if(v[k+1]==0, v[k+1]=km; m=k)); print1(0); for(i=1, NN, print1(", ", v[i])); } \\ Jinyuan Wang, Aug 04 2019


CROSSREFS

Similar in spirit to A181391.  N. J. A. Sloane, Aug 26 2019
Sequence in context: A233324 A268679 A128807 * A071628 A033809 A046067
Adjacent sequences: A309032 A309033 A309034 * A309036 A309037 A309038


KEYWORD

nonn


AUTHOR

Marc Morgenegg, Jul 08 2019


EXTENSIONS

More terms from Jinyuan Wang, Aug 04 2019


STATUS

approved



