

A328010


The 5x + 1 sequence beginning at 17.


3



17, 86, 43, 216, 108, 54, 27, 136, 68, 34, 17, 86, 43, 216, 108, 54, 27, 136, 68, 34, 17, 86, 43, 216, 108, 54, 27, 136, 68, 34, 17, 86, 43, 216, 108, 54, 27, 136, 68, 34, 17, 86, 43, 216, 108, 54, 27, 136, 68, 34, 17, 86, 43, 216, 108, 54, 27, 136, 68, 34, 17
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OFFSET

0,1


COMMENTS

The 5x+1 problem is similar to the 3x+1 or Collatz problem. For some starting values it is known that the 5x+1 trajectory will tend to infinity or enter a periodic orbit.
Alex V. Kontorovich & Jeffrey C. Lagarias conjectured that there are very few periodic orbits. One of them is shown here.
The two other known periodic orbits are given in the crossrefs.


LINKS

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,1).


FORMULA

a(n+1) = 5*a(n) + 1 if a(n) is odd, a(n+1) = a(n)/2 otherwise.
G.f.: (17 + 86*x + 43*x^2 + 216*x^3 + 108*x^4 + 54*x^5 + 27*x^6 + 136*x^7 + 68*x^8 + 34*x^9) / ((1  x)*(1 + x)*(1  x + x^2  x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)).
a(n) = a(n10) for n>9.
(End)


PROG

(PARI) Vec((17 + 86*x + 43*x^2 + 216*x^3 + 108*x^4 + 54*x^5 + 27*x^6 + 136*x^7 + 68*x^8 + 34*x^9) / ((1  x)*(1 + x)*(1  x + x^2  x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)) + O(x^60)) \\ Colin Barker, Oct 05 2019


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



