A225784 - OEIS

%I #15 Nov 02 2024 06:50:05

%S 1,2,240,4,80,80,272272,8,350064,80,38896,240,208,272272,4095840,16,

%T 3536,116688,21431696,80,1344,38896,1365280,80,535792400,208,

%U 44841486948146266934850832405421294927083491752830032389039800908293040266400,38896,1127984,1365280

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

%C 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,...

%C a(n) = denominator of Sum_{k = 1..A006577(n)} 1/A070165(n,k). - _Reinhard Zumkeller_, May 16 2013

%H Reinhard Zumkeller, <a href="/A225784/b225784.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%e 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.

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

%o (Haskell)

%o import Data.Ratio (denominator)

%o a225784 = denominator . sum . map (recip . fromIntegral) . a070165_row

%o -- _Reinhard Zumkeller_, May 16 2013

%Y Cf. A225761 (numerators), A087226.

%Y Cf. A225843.

%K nonn,changed

%O 1,2

%A _Nico Brown_, May 15 2013

%E Extended by _T. D. Noe_, May 15 2013