A008878 3x+1 sequence starting at 39.

39, 118, 59, 178, 89, 268, 134, 67, 202, 101, 304, 152, 76, 38, 19, 58, 29, 88, 44, 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

Offset

0,1

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 periodic sequences.

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

Formula

G.f.: (39 + 118*x + 59*x^2 + 139*x^3 - 29*x^4 + 209*x^5 - 44*x^6 - 22*x^7 - 66*x^8 - 33*x^9 + 237*x^10 - 50*x^11 - 25*x^12 - 266*x^13 - 133*x^14 - 18*x^15 - 9*x^16 + 69*x^17 - 14*x^18 - 7*x^19 - 77*x^20 - 10*x^21 - 5*x^22 + 41*x^23 - 8*x^24 - 4*x^25 - 12*x^26 - 6*x^27 - 3*x^28 - 35*x^29 - 4*x^30 - 2*x^31 - x^32 - 14*x^33 - 7*x^34)/(1 - x^3). - Charles R Greathouse IV, May 25 2026

Maple

f := proc(n) option remember; if n = 0 then 39; 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]&, 39, 100] (* Vincenzo Librandi, Jul 29 2014 *)

Prog

(Magma) [n eq 1 select 39 else IsOdd(Self(n-1)) select 3*Self(n-1)+1 else Self(n-1) div 2: n in [1..70]]; // Vincenzo Librandi, Jul 29 2014
(PARI) a(n)=if(n>31, 107\5^(n%3)%5, [39, 118, 59, 178, 89, 268, 134, 67, 202, 101, 304, 152, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8][n+1]) \\ Charles R Greathouse IV, May 25 2026

Crossrefs

Row 39 of A347270.

Sequence in context: A044226 A044607 A244694 * A249301 A239562 A044290

Adjacent sequences: A008875 A008876 A008877 * A008879 A008880 A008881

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved