

A075684


For odd numbers 2n1, the maximum number produced by iterating the reduced Collatz function R defined as R(k) = (3k+1)/2^r, with r as large as possible.


5



1, 5, 5, 17, 17, 17, 13, 53, 17, 29, 21, 53, 29, 3077, 29, 3077, 33, 53, 37, 101, 3077, 65, 45, 3077, 49, 77, 53, 3077, 65, 101, 61, 3077, 65, 101, 69, 3077, 3077, 113, 77, 269, 81, 3077, 85, 197, 101, 3077, 93, 3077, 3077, 149, 101, 3077, 269, 3077, 3077, 3077
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

See A075677 for the function R applied to the odd numbers once. See A075680 for the number of iterations required to yield 1. Sequence A006884, with the number 2 removed, gives the odd numbers that produce new record maxima. The maxima of the current sequence are related to A006885: if m is a maximum of the usual Collatz iteration, then (m1)/3 is the maximum for the reduced Collatz iteration.


LINKS



EXAMPLE

a(4) = 17 because 7 is the fourth odd number and 17 is the largest number in the iteration: R(7)=11, R(11)=17, R(17)=13, R(13)=5, R(5)=1.


MATHEMATICA

nextOddK[n_] := Module[{m=3n+1}, While[EvenQ[m], m=m/2]; m]; (* assumes odd n *) Table[m=n; maxK=n; If[n>1, While[m=nextOddK[m]; maxK=Max[m, maxK]; m!=1]]; maxK, {n, 1, 200, 2}]


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



