A033480 3x + 1 sequence beginning at 15.

15, 46, 23, 70, 35, 106, 53, 160, 80, 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, 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

Links

Colin Barker, Table of n, a(n) for n = 0..1000

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) = 15, a(n) = a(n - 1)/2 if a(n - 1) is even or 3a(n - 1) + 1 if a(n - 1) is odd.

From Colin Barker, Oct 04 2019: (Start)

G.f.: (15 + 46*x + 23*x^2 + 55*x^3 - 11*x^4 + 83*x^5 - 17*x^6 + 125*x^7 - 26*x^8 - 13*x^9 - 140*x^10 - 70*x^11 - 35*x^12 - 4*x^13 - 2*x^14 - x^15 - 14*x^16 - 7*x^17) / ((1 - x)*(1 + x + x^2)).

a(n) = a(n-3) for n>17.

(End)

Example

15 is odd, so the next term is 3 * 15 + 1 = 46.
46 is even, so the next term is 46/2 = 23.

Mathematica

NestList[If[EvenQ[#], #/2, 3# + 1] &, 15, 100] (* Harvey P. Dale, Dec 27 2011 *)

Prog

(PARI) a(n)=my(k=15); for(i=1, n, k=if(k%2, k/2, 3*k+1)); k \\ Charles R Greathouse IV, May 04 2015
(PARI) Vec((15 + 46*x + 23*x^2 + 55*x^3 - 11*x^4 + 83*x^5 - 17*x^6 + 125*x^7 - 26*x^8 - 13*x^9 - 140*x^10 - 70*x^11 - 35*x^12 - 4*x^13 - 2*x^14 - x^15 - 14*x^16 - 7*x^17) / ((1 - x)*(1 + x + x^2)) + O(x^80)) \\ Colin Barker, Oct 04 2019

Crossrefs

Cf. A033479.

Row 15 of A347270.

Sequence in context: A068513 A267079 A290583 * A041434 A136430 A139278

Adjacent sequences: A033477 A033478 A033479 * A033481 A033482 A033483

Keyword

nonn,easy

Author

Jeff Burch

Status

approved