cp's OEIS Frontend

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).

%I A306246 #18 Jun 28 2019 21:15:57
%S A306246 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,
%T A306246 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,
%U A306246 9,10,13,9,15,11,5,15,13,8,15,12,5,14,13,8
%N 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).
%C A306246 The sequence o corresponds to the ordinal transform of the sequence a.
%C A306246 This sequence has a taste of Fibonacci, as each pair of consecutive terms gives rise to the next term.
%C A306246 This sequence is unbounded:
%C A306246 - 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.
%C A306246 This sequence has interesting graphical features (see Links section).
%H A306246 Rémy Sigrist, <a href="/A306246/b306246.txt">Table of n, a(n) for n = 1..10000</a>
%H A306246 Rémy Sigrist, <a href="/A306246/a306246.png">Density plot of the first 10000000 terms</a>
%e A306246 The first terms, alongside o, are:
%e A306246   n   a(n)  o(n)
%e A306246   --  ----  ----
%e A306246    1     1     1
%e A306246    2     2     1
%e A306246    3     2     2
%e A306246    4     3     1
%e A306246    5     3     2
%e A306246    6     3     3
%e A306246    7     5     1
%e A306246    8     4     1
%e A306246    9     2     3
%e A306246   10     4     2
%e A306246   11     5     2
%e A306246   12     4     3
%e A306246   13     5     3
%e A306246   14     6     1
%e A306246   15     4     4
%e A306246   16     5     4
%e A306246   17     8     1
%e A306246   18     5     5
%e A306246   19     6     2
%e A306246   20     7     1
%o A306246 (PARI) o = vector(18); for (n=1, 79, if (n<=2, v=n, v=pp+p); print1 (v ", "); [pp,p]=[p,o[1+v]++])
%Y A306246 See A306251 for the ordinal transform of this sequence.
%K A306246 nonn
%O A306246 1,2
%A A306246 _Rémy Sigrist_, Jan 31 2019