A075684 For odd numbers 2n-1, 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.

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

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 (m-1)/3 is the maximum for the reduced Collatz iteration.

Links

T. D. Noe, Table of n, a(n) for n = 1..5000

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

Cf. A006884, A006885, A075677, A075680.

Sequence in context: A214022 A125256 A228564 * A146876 A147206 A146852

Adjacent sequences: A075681 A075682 A075683 * A075685 A075686 A075687

Keyword

easy,nonn

Author

T. D. Noe, Sep 25 2002

Status

approved