A008882 3x+1 sequence starting at 99.

99, 298, 149, 448, 224, 112, 56, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for sequences related to 3x+1 (or Collatz) problem
• Index entries for linear recurrences with constant coefficients, signature (0,0,1).

Crossrefs

Row 99 of A347270.

Programs

Magma

[n eq 1 select 99 else IsOdd(Self(n-1)) select 3*Self(n-1)+1 else Self(n-1) div 2: n in [1..80]]; // Vincenzo Librandi, Jul 29 2014

Maple

f := proc(n) option remember; if n = 0 then 99; 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]&,99,70] (* Harvey P. Dale, Jul 28 2014 *)

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(99,60)) \\ A008882 (from 99 first 60)
\\ Anatoly E. Voevudko, Mar 26 2016