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A306246 a(1) = 1, a(2) = 2, and for any n > 2, a(n) = o(n-1) + o(n-2) 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 (list; graph; refs; listen; history; text; internal format)
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 M-th 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

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)