

A359728


a(1) = 1; a(n) is the smallest positive number not among the first k terms where k is the number of times a(n1) has occurred.


1



1, 2, 2, 3, 2, 3, 3, 3, 4, 2, 4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 5, 2, 4, 5, 3, 4, 5, 3, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 2, 4, 5, 6, 3, 5, 6, 3, 5, 6, 4, 5, 6, 4, 5, 6, 4, 6, 4, 6, 4, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6
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OFFSET

1,2


COMMENTS

A new number is always followed by a 2.


LINKS



EXAMPLE

a(4) is 3 because the previous term (2) appears two times; we therefore look at the first 2 terms (1,2). 3 is the smallest number not among them, so a(4) is 3.
a(21) is 5: We see that a(20)=4 appears 9 times; the smallest number not among the first 9 terms (1,2,2,3,2,3,3,3,4) is 5.


MATHEMATICA

K = {1}; While[Length@K < 87, T = Take[K, Count[K, Last@K]]; i = 1; While[MemberQ[T, i], i++]; AppendTo[K, i]]; Print[K] (* Samuel Harkness, Mar 12 2023 *)


PROG

(PARI) lista(nn) = my(va=vector(nn)); va[1] = 1; for (n=2, nn, my(k=#select(x>(x==va[n1]), va)); my(vb=Vec(va, k), m); for(j=1, vecmax(vb)+1, if (! #select(x>(x==j), vb), m=j; break)); va[n] = m; ); va; \\ Michel Marcus, Jan 13 2023


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



