A008877 3x+1 sequence starting at 57.

57, 172, 86, 43, 130, 65, 196, 98, 49, 148, 74, 37, 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

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.: (57 + 172*x + 86*x^2 - 14*x^3 - 42*x^4 - 21*x^5 + 153*x^6 - 32*x^7 - 16*x^8 - 48*x^9 - 24*x^10 - 12*x^11 - 36*x^12 - 18*x^13 - 9*x^14 - 98*x^15 - 49*x^16 - 6*x^17 - 3*x^18 + 27*x^19 - 5*x^20 + 41*x^21 - 8*x^22 - 4*x^23 - 12*x^24 - 6*x^25 - 3*x^26 - 35*x^27 - 4*x^28 - 2*x^29 - x^30 - 14*x^31 - 7*x^32)/(1 - x^3). - Charles R Greathouse IV, May 25 2026

Maple

f := proc(n) option remember; if n = 0 then 57; 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]&, 57, 100] (* Vincenzo Librandi, Jul 29 2014 *)

Prog

(Haskell)
a008877 n = a008877_list !! n
a008877_list = 57 : iterate a006370 57
-- Reinhard Zumkeller, Aug 30 2012
(Magma) [n eq 1 select 57 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
(PARI) a(n)=if(n>29, [4, 2, 1][n%3+1], [57, 172, 86, 43, 130, 65, 196, 98, 49, 148, 74, 37, 112, 56, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8][n+1]) \\ Charles R Greathouse IV, May 25 2026

Crossrefs

Cf. A006370.

Row 57 of A347270.

Sequence in context: A044389 A044770 A389180 * A381766 A338078 A376538

Adjacent sequences: A008874 A008875 A008876 * A008878 A008879 A008880

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved