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A033480 3x + 1 sequence beginning at 15. 1
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 (list; graph; refs; listen; history; text; internal format)
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.

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

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Last modified July 9 11:06 EDT 2020. Contains 335543 sequences. (Running on oeis4.)