The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A185816 Number of iterations of lambda(n) needed to reach 1. 6
 0, 1, 2, 2, 3, 2, 3, 2, 3, 3, 4, 2, 3, 3, 3, 3, 4, 3, 4, 3, 3, 4, 5, 2, 4, 3, 4, 3, 4, 3, 4, 3, 4, 4, 3, 3, 4, 4, 3, 3, 4, 3, 4, 4, 3, 5, 6, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 5, 3, 4, 4, 3, 4, 3, 4, 5, 4, 5, 3, 4, 3, 4, 4, 4, 4, 4, 3, 4, 3, 5, 4, 5, 3, 4, 4, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS lambda(n) is the Carmichael lambda function, A002322. a(n) = (length of row n in table A246700) - 1. - Reinhard Zumkeller, Sep 02 2014 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 Paul Erdős, Andrew Granville, Carl Pomerance, and Claudia Spiro, On the normal behavior of the iterates of some arithmetic functions, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204. Paul Erdős, Andrew Granville, Carl Pomerance, and Claudia Spiro, On the normal behavior of the iterates of some arithmetic functions, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204. [Annotated copy with A-numbers] Paul Erdős, A. Granville, C. Pomerance, and C. Spiro, On the Normal Behavior of the Iterates of some Arithmetic Functions, in Analytic number theory (Allerton Park, IL, 1989), Progr. Math., 85 Birkhäuser Boston, Boston, MA, (1990), 165-204. Nick Harland, The iterated Carmichael lambda function, arXiv:1111.3667v1 [math.NT], Nov 15, 2011. Nick Harland, The number of iterates of the Carmichael lambda function required to reach 1, arXiv:1203.4791 [math.NT], Mar 21, 2012. FORMULA For n > 1: a(n) = a(A002322(n)) + 1. - Reinhard Zumkeller, Sep 02 2014 EXAMPLE If n = 23 the trajectory is 23, 22, 10, 4, 2, 1. Its length is 6, thus a(23) = 5. MAPLE a:= n-> `if`(n=1, 0, 1+a(numtheory[lambda](n))): seq(a(n), n=1..100); # Alois P. Heinz, Apr 27 2019 MATHEMATICA f[n_] := Length[ NestWhileList[ CarmichaelLambda, n, Unequal, 2]] - 2; Table[f[n], {n, 1, 120}] PROG (Haskell) a185816 n = if n == 1 then 0 else a185816 (a002322 n) + 1 -- Reinhard Zumkeller, Sep 02 2014 CROSSREFS Cf. A002322, A036459, A003434. Cf. A027763, A173927, A246700. Sequence in context: A350065 A077982 A331921 * A324901 A295568 A099427 Adjacent sequences: A185813 A185814 A185815 * A185817 A185818 A185819 KEYWORD nonn AUTHOR Michel Lagneau, Feb 05 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 26 09:40 EDT 2024. Contains 372824 sequences. (Running on oeis4.)