login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A225761 Numerators of the sums of reciprocals of the Collatz (3x+1) sequence beginning with n and stopping at 1. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A203748 A329706 A229748 * 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 8 21:44 EDT 2020. Contains 333329 sequences. (Running on oeis4.)