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3x + 1 sequence beginning at 15.
3

%I #24 Nov 17 2021 17:01:27

%S 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,

%T 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,

%U 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

%N 3x + 1 sequence beginning at 15.

%H Colin Barker, <a href="/A033480/b033480.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).

%F 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.

%F From _Colin Barker_, Oct 04 2019: (Start)

%F 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)).

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

%F (End)

%e 15 is odd, so the next term is 3 * 15 + 1 = 46.

%e 46 is even, so the next term is 46/2 = 23.

%t NestList[If[EvenQ[#], #/2, 3# + 1] &, 15, 100] (* _Harvey P. Dale_, Dec 27 2011 *)

%o (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

%o (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

%Y Cf. A033479.

%Y Row 15 of A347270.

%K nonn,easy

%O 0,1

%A _Jeff Burch_