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A346213
Number of iterations of A000688 needed to reach 1 starting at n (n is counted).
1
1, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 2, 2, 3, 3, 2, 3, 3, 2, 2, 2, 3, 2, 2, 2, 4, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2, 3, 3, 3, 2, 3, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 3, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 3, 3, 2, 2, 2, 3, 3, 2, 2, 3, 2, 2, 2
OFFSET
1,2
COMMENTS
The least value of n such that a(n) = 1, 2, ..., 5 is 1, 2, 4, 36 and 264600.
LINKS
Paul Erdős and Aleksandar Ivić, On the iterates of the enumerating function of finite abelian groups, Bulletin Académie serbe des sciences et des arts, Classe des sciences mathématiques et naturelles, Sciences mathématiques, No. 17 (1989), pp. 13-22; alternative link.
FORMULA
Sum_{k<=x} a(k) ~ c*x + O(x^(1/2 + eps)), where c > 1 is a constant (Erdős and Ivić, 1989).
EXAMPLE
a(4) = 3 since the trajectory of n = 4, {n, A000688(n), A000688(A000688(n))} = {4, 2, 1}, has the length 3.
MATHEMATICA
a[n_] := -1 + Length @ FixedPointList[FiniteAbelianGroupCount, n]; Array[a, 100]
CROSSREFS
Sequence in context: A104517 A098397 A278744 * A082091 A375431 A334216
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jul 10 2021
STATUS
approved