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A364784
a(n) = n for n <= 2. Thereafter if a(n-1) is a novel term, a(n) = a(a(k)) where k is the greatest prior term < a(n-1); otherwise, a(n) = number of times a(n-1) has been repeated.
1
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, 14, 1, 15, 5, 3, 6, 2, 10, 1, 16, 1, 17, 6, 3, 7, 2, 11, 1, 18, 2, 12, 1, 19, 4, 4, 5, 4, 6, 4, 7, 3, 8, 2
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, 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
Sequence in context: A285813 A236480 A236508 * A239000 A105248 A289495
KEYWORD
nonn,tabf
AUTHOR
EXTENSIONS
More terms from Michael De Vlieger, Aug 07 2023
STATUS
approved