

A075680


For odd numbers 2n1, the minimum number of iterations of the reduced Collatz function R required to yield 1. The function R is defined as R(k) = (3k+1)/2^r, with r as large as possible.


15



0, 2, 1, 5, 6, 4, 2, 5, 3, 6, 1, 4, 7, 41, 5, 39, 8, 3, 6, 11, 40, 9, 4, 38, 7, 7, 2, 41, 10, 10, 5, 39, 8, 8, 3, 37, 42, 3, 6, 11, 6, 40, 1, 9, 9, 33, 4, 38, 43, 7, 7, 31, 12, 36, 41, 24, 2, 10, 5, 10, 34, 15, 39, 15, 44, 8, 8, 13, 32, 13, 3, 37, 42, 42, 6, 3, 11, 30, 11, 18, 35, 6, 40, 23
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OFFSET

1,2


COMMENTS

See A075677 for the function R applied to the odd numbers once. The 3x+1 conjecture asserts that a(n) is a finite number for all n. The function R applied to the odd numbers shows the essential behavior of the 3x+1 iterations.
Bisection of A006667.  T. D. Noe, Jun 01 2006


LINKS

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


EXAMPLE

a(4) = 5 because 7 is the fourth odd number and 5 iterations are needed: R(R(R(R(R(7)))))=1.


MATHEMATICA

nextOddK[n_] := Module[{m=3n+1}, While[EvenQ[m], m=m/2]; m]; (* assumes odd n *) Table[m=n; cnt=0; If[n>1, While[m=nextOddK[m]; cnt++; m!=1]]; cnt, {n, 1, 200, 2}]


PROG

(Haskell)
a075680 n = snd $ until ((== 1) . fst)
(\(x, i) > (a000265 (3 * x + 1), i + 1)) (2 * n  1, 0)
 Reinhard Zumkeller, Jan 08 2014


CROSSREFS

Cf. A075677.
See A075684 for the largest number attained during the iteration.
Cf. A000265.
Sequence in context: A073474 A067311 A162750 * A192024 A249283 A176035
Adjacent sequences: A075677 A075678 A075679 * A075681 A075682 A075683


KEYWORD

easy,nonn


AUTHOR

T. D. Noe, Sep 25 2002


STATUS

approved



