|
%I #48 Aug 06 2022 02:24:19
%S 27,82,41,124,62,31,94,47,142,71,214,107,322,161,484,242,121,364,182,
%T 91,274,137,412,206,103,310,155,466,233,700,350,175,526,263,790,395,
%U 1186,593,1780,890,445,1336,668,334,167,502,251,754,377,1132,566,283,850,425,1276,638,319,958,479,1438,719,2158,1079
%N 3x+1 sequence starting at 27.
%C 27=A060412(4); a(A006577(27))=a(111)=1; a(n)=A161021(n+59) for n with 103<=n<=111. - _Reinhard Zumkeller_, Jun 03 2009
%C At step 109 enters the loop 4 2 1 4 2 1 4 2 1 ... - _N. J. A. Sloane_, Jul 27 2019
%D R. K. Guy, Unsolved Problems in Number Theory, E16.
%D H.-O. Peitgen et al., Chaos and Fractals, Springer, p. 33.
%H T. D. Noe, <a href="/A008884/b008884.txt">Table of n, a(n) for n = 0..111</a>
%H F. Oort, <a href="http://www.math.uu.nl/~oort0109/Oort3Taiwan-PrimeNu-2013.pdf">Prime numbers</a>, 2013, ICCM Notices, Talk at Academia Sinica and National Taiwan University, 17-XII-2012.
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%F a(0) = 27, a(n) = 3*a(n-1)+1 if a(n-1) is odd, a(n) = a(n-1)/2 if a(n-1) is even. - _Vincenzo Librandi_, Dec 24 2010; corrected by _Klaus Brockhaus_, Dec 25 2010
%p f := proc(n) option remember; if n = 0 then 27; elif f(n-1) mod 2 = 0 then f(n-1)/2 else 3*f(n-1)+1; fi; end;
%t NestList[If[EvenQ[#],#/2,3#+1]&,27,70] (* _Harvey P. Dale_, Jun 30 2011 *)
%o (Magma) [ n eq 1 select 27 else IsOdd(Self(n-1)) select 3*Self(n-1)+1 else Self(n-1) div 2: n in [1..70] ]; // _Klaus Brockhaus_, Dec 25 2010
%o (PARI) Collatz(n,lim=0)={
%o my(c=n,e=0,L=List(n)); if(lim==0, e=1; lim=n*10^6);
%o for(i=1,lim, if(c%2==0, c=c/2, c=3*c+1); listput(L,c); if(e&&c==1, break));
%o return(Vec(L)); }
%o print(Collatz(27)) \\ A008884 (from 27 to the first 1)
%o \\ _Anatoly E. Voevudko_, Mar 26 2016
%Y Cf. A161022, A161023.
%Y Row 27 of A347270.
%K nonn,nice,easy
%O 0,1
%A _N. J. A. Sloane_
%E More terms from Larry Reeves (larryr(AT)acm.org), Apr 27 2001
|
