

A306246


a(1) = 1, a(2) = 2, and for any n > 2, a(n) = o(n1) + o(n2) where o(k) is the number of occurrences of a(k) among a(1), ..., a(k).


3



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

1,2


COMMENTS

The sequence o corresponds to the ordinal transform of the sequence a.
This sequence has a taste of Fibonacci, as each pair of consecutive terms gives rise to the next term.
This sequence is unbounded:
 if the sequence was bounded, say a(n) <= M for any n > 0, then some value in the range 1..M, say t, would appear at least M times among the first M^2 terms, and we would have a value > M after the Mth occurrence of t, a contradiction.
This sequence has interesting graphical features (see Links section).


LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Density plot of the first 10000000 terms


EXAMPLE

The first terms, alongside o, are:
n a(n) o(n)
  
1 1 1
2 2 1
3 2 2
4 3 1
5 3 2
6 3 3
7 5 1
8 4 1
9 2 3
10 4 2
11 5 2
12 4 3
13 5 3
14 6 1
15 4 4
16 5 4
17 8 1
18 5 5
19 6 2
20 7 1


PROG

(PARI) o = vector(18); for (n=1, 79, if (n<=2, v=n, v=pp+p); print1 (v ", "); [pp, p]=[p, o[1+v]++])


CROSSREFS

See A306251 for the ordinal transform of this sequence.
Sequence in context: A136545 A125843 A210957 * A147665 A222820 A301662
Adjacent sequences: A306243 A306244 A306245 * A306247 A306248 A306249


KEYWORD

nonn


AUTHOR

Rémy Sigrist, Jan 31 2019


STATUS

approved



