OFFSET
1,2
COMMENTS
The definition is similar to that of A364749.
With the exception of a(3) = a(4) = 1, every term a(r-1) = 1 occurs prior to record term a(r), and a(r) is the number of times 1 has been repeated so far.
The subsequence of records is A000027, and the subsequence {a(r)} is a copy of the sequence itself, which is fractal (see Example).
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^16.
EXAMPLE
The given terms are a(1) = 1 and a(2) = 2. Since 2 is a novel term and 1 is the greatest prior term < 2, a(3) = a(1) = 1, and since a(3) is the second occurrence of 1, a(4) = 1 (the number of times 1 has been repeated). Now 1 has occurred 3 times so a(5) = 2, and so on.
The sequence can be represented as an irregular table in which the n-th row starts with the n-th record, and ends with the term = 1 which precedes the next record. Thus the first column is A000027, and the second column is the sequence itself.
The table begins:
1;
2,1,1,2,1;
3,2,2,3,1;
4,1;
5,1;
6,2,4,1;
7,1;
8,3,2,5,1;
9,2,6,1;
10,2,7,1;
11,3,3,4,2,8,1;
12,1;
13,4,3,5,2,9,1;
MATHEMATICA
nn = 1000; c[_] = 0; Array[Set[a[#], #] &, 2]; c[1] = 1; Do[a[n] = If[c[#] == 0, c[#]++; k = # - 1; While[c[k] == 0, k--]; a[k], c[#]; c[#]++] &@ a[n - 1], {n, 3, nn}], n]; Array[a, nn] (* Michael De Vlieger, Aug 07 2023 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
David James Sycamore, Aug 07 2023
EXTENSIONS
More terms from Michael De Vlieger, Aug 07 2023
STATUS
approved