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A075680
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For odd numbers 2n-1, 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.
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8
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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 (noe(AT)sspectra.com), Jun 01 2006
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..5000
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EXAMPLE
| a(4) = 5 because 7 is the fourth odd number and 5 iterations are needed: R(R(R(R(R(7)))))=1.
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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}]
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CROSSREFS
| Cf. A075677.
See A075684 for the largest number attained during the iteration.
Sequence in context: A073474 A067311 A162750 * A192024 A176035 A190992
Adjacent sequences: A075677 A075678 A075679 * A075681 A075682 A075683
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KEYWORD
| easy,nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Sep 25 2002
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