cp's OEIS Frontend

A075426 Smallest initial value k that reaches 1 in n steps when iterating the map m -> rad(m)-1, where rad(m) is the squarefree kernel of m (A007947).

%I A075426 #25 Aug 21 2013 19:52:05
%S A075426 1,2,3,6,7,14,15,30,31,62,95,318,319,734,959,2798,2879,5758,5759,
%T A075426 11518,11519,23038,23039,46078,46079,92158,92159,184318,184319,368638,
%U A075426 368639,737278,737279,1548286,1548287,3096574,5160959,10321918,10321919
%N A075426 Smallest initial value k that reaches 1 in n steps when iterating the map m -> rad(m)-1, where rad(m) is the squarefree kernel of m (A007947).
%C A075426 Least k such that A075425(k) = n;
%C A075426 Observations: a(n) = n mod 2; frequently a(2k)+1 = a(2k+1) and a(2k) = 2*a(2k-1). a(n)=A075427(n-1) for n<=9.
%C A075426 Also A110157(a(n)) = n and A110157(m) < n for m < a(n).
%H A075426 Charles R Greathouse IV and Donovan Johnson, <a href="/A075426/b075426.txt">Table of n, a(n) for n = 0..56</a> (terms up to a(50) from Charles R Greathouse IV)
%o A075426 (PARI) rad(n)=my(f=factor(n)[, 1]); prod(i=1, #f, f[i])
%o A075426 A075425(n)=if(n<4, n, 1+A075425(rad(n)-1))
%o A075426 r=0;for(n=1,1e8,t=A075425(n);if(t>r,r=t;print1(n", "))) \\ _Charles R Greathouse IV_, Aug 08 2013
%o A075426 (Haskell)
%o A075426 import Data.List (elemIndex); import Data.Maybe (fromJust)
%o A075426 a075426 = (+ 1) . fromJust . (`elemIndex` a075425_list)
%o A075426 -- _Reinhard Zumkeller_, Aug 14 2013
%K A075426 nonn
%O A075426 0,2
%A A075426 _Reinhard Zumkeller_, Sep 15 2002
%E A075426 a(33)-a(38) from _Donovan Johnson_, Aug 27 2010