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

Author

T. D. Noe, Sep 25 2002

Keywords

• easy
• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A006884, A006885, A075677, A075680.

Programs

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}]