This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A182850 a(n) = number of iterations that n requires to reach a fixed point under the x -> A181819(x) map. 87
 0, 0, 1, 2, 1, 3, 1, 2, 2, 3, 1, 4, 1, 3, 3, 2, 1, 4, 1, 4, 3, 3, 1, 4, 2, 3, 2, 4, 1, 3, 1, 2, 3, 3, 3, 3, 1, 3, 3, 4, 1, 3, 1, 4, 4, 3, 1, 4, 2, 4, 3, 4, 1, 4, 3, 4, 3, 3, 1, 5, 1, 3, 4, 2, 3, 3, 1, 4, 3, 3, 1, 4, 1, 3, 4, 4, 3, 3, 1, 4, 2, 3, 1, 5, 3, 3, 3, 4, 1, 5, 3, 4, 3, 3, 3, 4, 1, 4, 4, 3, 1, 3, 1, 4, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The fixed points of the x -> A181819(x) map are 1 and 2. Note that the x -> A000005(x) map has the same fixed points, and that A000005(n) = A181819(n) iff n is cubefree (cf. A004709). Under the x -> A181819(x) map, it seems significantly easier to generalize about which kinds of integers take a given number of iterations to reach a fixed point than under the x -> A000005(x) map. Also the number of steps in the reduction of the multiset of prime factors of n wherein one repeatedly takes the multiset of multiplicities. For example, the a(90) = 5 steps are {2,3,3,5} -> {1,1,2} -> {1,2} -> {1,1} -> {2} -> {1}. - Gus Wiseman, May 13 2018 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Fixed Point Eric Weisstein's World of Mathematics, Map FORMULA For n > 2, a(n) = a(A181819(n)) + 1. a(n) = 0 iff n equals 1 or 2. a(n) = 1 iff n is an odd prime (A000040(n) for n>1). a(n) = 2 iff n is a composite perfect prime power (A025475(n) for n>1). a(n) = 3 iff n is a squarefree composite integer or a power of a squarefree composite integer (cf. A182853). a(n) = 4 iff n's prime signature a) contains at least two distinct numbers, and b) contains no number that occurs less often than any other number (cf. A182854). EXAMPLE A181819(6) = 4; A181819(4) = 3; A181819(3) = 2; A181819(2) = 2. Therefore, a(6) = 3, a(4) = 2, a(3)= 1, and a(2) = 0. MATHEMATICA Table[If[n<=2, 0, Length[FixedPointList[Sort[Length/@Split[#]]&, Sort[Last/@FactorInteger[n]]]]-1], {n, 100}] (* Gus Wiseman, May 13 2018 *) PROG (Haskell) a182850 n = length \$ takeWhile (`notElem` [1, 2]) \$ iterate a181819 n -- Reinhard Zumkeller, Mar 26 2012 (Scheme, with memoization-macro definec) (definec (A182850 n) (if (<= n 2) 0 (+ 1 (A182850 (A181819 n))))) ;; Antti Karttunen, Feb 05 2016 CROSSREFS A182857 gives values of n where a(n) increases to a record. Cf. A000961, A001222, A003434, A005117, A007916, A036459, A112798, A130091, A181819, A182851-A182858, A238748, A304455, A304464, A304465. Sequence in context: A305818 A303757 A323014 * A293227 A291208 A241165 Adjacent sequences:  A182847 A182848 A182849 * A182851 A182852 A182853 KEYWORD nonn AUTHOR Matthew Vandermast, Jan 04 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 17 11:41 EDT 2019. Contains 328108 sequences. (Running on oeis4.)