A008884 3x+1 sequence starting at 27.

27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 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

Offset

0,1

Comments

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

At step 109 enters the loop 4 2 1 4 2 1 4 2 1 ... - N. J. A. Sloane, Jul 27 2019

References

R. K. Guy, Unsolved Problems in Number Theory, E16.

H.-O. Peitgen et al., Chaos and Fractals, Springer, p. 33.

Links

T. D. Noe, Table of n, a(n) for n = 0..111

F. Oort, Prime numbers, 2013, ICCM Notices, Talk at Academia Sinica and National Taiwan University, 17-XII-2012.

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

Index entries for linear recurrences with constant coefficients, signature (0,0,1).

Formula

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

Maple

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;

Mathematica

NestList[If[EvenQ[#], #/2, 3#+1]&, 27, 70] (* Harvey P. Dale, Jun 30 2011 *)

Prog

(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
(PARI) Collatz(n, lim=0)={
my(c=n, e=0, L=List(n)); if(lim==0, e=1; lim=n*10^6);
for(i=1, lim, if(c%2==0, c=c/2, c=3*c+1); listput(L, c); if(e&&c==1, break));
return(Vec(L)); }
print(Collatz(27)) \\ A008884 (from 27 to the first 1)
\\ Anatoly E. Voevudko, Mar 26 2016

Crossrefs

Cf. A161022, A161023.

Row 27 of A347270.

Sequence in context: A292872 A057609 A255624 * A031455 A045004 A042432

Adjacent sequences: A008881 A008882 A008883 * A008885 A008886 A008887

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Apr 27 2001

Status

approved