OFFSET
0,1
COMMENTS
A number is considered to be its own zeroth iteration.
Is the sequence defined for all n? If so, are there infinitely many composite numbers? If not, are infinitely many a(n) defined?
From Hartmut F. W. Hoft, Apr 05 2016: (Start)
Numbers a(6)...a(11) and a(12)...a(23) each belong to iteration sequences that start with prime numbers 10039 and 23023727, respectively, while the other numbers in the sequences are composite.
For the entire iteration sequences and computation of the additional numbers for this sequence see A271363. (End)
For n>1, a(n) is the least integer k such that the repeated application of x -> A073846(x) strictly decreases exactly n times in a row. - Hugo Pfoertner and Michel Marcus, Mar 11 2021
LINKS
Martin Ehrenstein, Table of n, a(n) for n = 0..43
FORMULA
For n>0, a(n+1) >= A073898(b(a(n))), where b(m) is the smallest odd composite not smaller than m, equality always holds if a(n) is composite.
EXAMPLE
MATHEMATICA
(* Since A073846(9)=9, search starts with 11 *)
c25000000 = Select[Range[25000000], CompositeQ];
a073846[n_] := c25000000[[Floor[n/2]]]
a073846Nest[n_] := Length[NestWhileList[a073846, n, OddQ]]
a263570[n_] := Module[{list={2, 3}, i, length}, For[i=11, i<=n, i+=2, length=a073846Nest[i]; If[Length[list]<length, AppendTo[list, i]]]; list]
a263570[25000000] (* original sequence data *)
(* Hartmut F. W. Hoft, Apr 05 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Chayim Lowen, Oct 21 2015
EXTENSIONS
a(24)-a(31) from Hartmut F. W. Hoft, Apr 05 2016
STATUS
approved