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).

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

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