A225784 Denominators of the sum of the reciprocals of the Collatz (3x+1) sequence beginning at n.

1, 2, 240, 4, 80, 80, 272272, 8, 350064, 80, 38896, 240, 208, 272272, 4095840, 16, 3536, 116688, 21431696, 80, 1344, 38896, 1365280, 80, 535792400, 208, 44841486948146266934850832405421294927083491752830032389039800908293040266400, 38896, 1127984, 1365280

Offset

1,2

Comments

If the sum of the reciprocals of a Collatz sequence is bounded, there are no Collatz cycles other than 4,2,1,4,2,1,...

a(n) = denominator of sum (1/A070165(n,k): k = 1..A006577(n)). - Reinhard Zumkeller, May 16 2013

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences related to 3x+1 (or Collatz) problem

Example

For n=9 the Collatz sequence is {9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 4, 2, 1}.  So the sum of the reciprocals is 1/9 + 1/28 + 1/14 + 1/7 + 1/22 + 1/11 + ... + 1/4 + 1/2 + 1/1 = 1061683/350064, whose denominator is 350064.

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Table[Denominator[Total[1/Collatz[n]]], {n, 40}] (* T. D. Noe, May 15 2013 *)

Prog

(Haskell)
import Data.Ratio (denominator)
a225784 = denominator . sum . map (recip . fromIntegral) . a070165_row
-- Reinhard Zumkeller, May 16 2013

Crossrefs

Cf. A225761 numerators), A087226.

Cf. A225843.

Sequence in context: A013477 A013473 A212839 * A087226 A217972 A071967

Adjacent sequences: A225781 A225782 A225783 * A225785 A225786 A225787

Keyword

nonn

Author

Nico Brown, May 15 2013

Extensions

Extended by T. D. Noe, May 15 2013

Status

approved