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

Author

Jeff Burch

Keywords

• nonn
• easy

Examples

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

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).

Crossrefs

Cf. A033479.

Row 15 of A347270.

Programs

Mathematica

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

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

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)