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A008884 3x+1 sequence starting at 27. 10
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 (list; graph; refs; listen; history; text; internal format)
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

REFERENCES

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

F. Oort, Prime numbers, 2013, http://www.math.uu.nl/~oort0109/Taiwan-PrimeNu2012-2013.pdf

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

LINKS

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

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.

Sequence in context: A216438 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

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Last modified September 25 21:33 EDT 2017. Contains 292500 sequences.