A225761 Numerators of the sums of reciprocals of the Collatz (3x+1) sequence beginning with n and stopping at 1.

1, 3, 617, 7, 171, 219, 766329, 15, 1061683, 179, 102151, 677, 497, 785777, 10380059, 31, 8861, 360377, 60226515, 183, 2731, 103919, 3339321, 229, 1548244271, 505, 129481899470258402665619129356105706380861444925035330406812603986229803685477, 113643

Offset

1,2

Comments

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

a(n) = numerator 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 numerator is 1061683.

Mathematica

Table[Numerator[Total[1/Collatz[n]]], {n, 40}] (* T. D. Noe, May 15 2013 *)

Prog

(Haskell)
import Data.Ratio (numerator)
a225761 = numerator . sum . map (recip . fromIntegral) . a070165_row
-- Reinhard Zumkeller, May 16 2013

Crossrefs

Cf. A087226, A225784 (denominators).

Cf. A225843.

Sequence in context: A329706 A229748 A368685 * A140029 A161964 A229688

Adjacent sequences: A225758 A225759 A225760 * A225762 A225763 A225764

Keyword

nonn

Author

Nico Brown, May 14 2013

Extensions

Extended by T. D. Noe, May 15 2013

Status

approved