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A057688 Trajectory of 5 under the '5x+1' map. 10
5, 26, 13, 66, 33, 11, 56, 28, 14, 7, 36, 18, 9, 3, 1, 6, 3, 1, 6, 3, 1, 6, 3, 1, 6, 3, 1, 6, 3, 1, 6, 3, 1, 6, 3, 1, 6, 3, 1, 6, 3, 1, 6, 3, 1, 6, 3, 1, 6, 3, 1, 6, 3, 1, 6, 3, 1, 6, 3, 1, 6, 3, 1, 6, 3, 1, 6, 3, 1, 6, 3, 1, 6, 3, 1, 6, 3, 1, 6, 3, 1, 6, 3, 1, 6, 3, 1, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The 'Px + 1 map': if x is divisible by any prime less than P then divide out these primes one at a time starting with the smallest; otherwise multiply x by P and add 1. This is similar to A057684, but with P = 5 instead of P = 13. - Alonso del Arte, Jul 04 2015

LINKS

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

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

FORMULA

a(0) = 5, a(n) = a(n - 1)/2 if a(n - 1) is even, a(n) = a(n - 1)/3 if a(n - 1) is odd and divisible by 3, a(n) = 5a(n - 1) otherwise.

From Colin Barker, Oct 10 2019: (Start)

G.f.: (5 + 26*x + 13*x^2 + 61*x^3 + 7*x^4 - 2*x^5 - 10*x^6 - 5*x^7 + 3*x^8 - 49*x^9 + 8*x^10 + 4*x^11 + 2*x^12 - 33*x^13 - 17*x^14 - 3*x^15) / ((1 - x)*(1 + x + x^2)).

a(n) = a(n-3) for n>15.

(End)

EXAMPLE

7 is odd and not divisible by 3, so it's followed by 5 * 7 + 1 = 36.

36 is even, so it's followed by 36/2 = 18.

18 is even, so it's followed by 18/2 = 9.

9 is odd and divisible by 3, so it's followed by 9/3 = 3.

MATHEMATICA

NestList[If[EvenQ[#], #/2, If[Mod[#, 3] == 0, #/3, 5# + 1]] &, 5, 100] (* Alonso del Arte, Jul 04 2015 *)

PROG

(PARI) Vec((5 + 26*x + 13*x^2 + 61*x^3 + 7*x^4 - 2*x^5 - 10*x^6 - 5*x^7 + 3*x^8 - 49*x^9 + 8*x^10 + 4*x^11 + 2*x^12 - 33*x^13 - 17*x^14 - 3*x^15) / ((1 - x)*(1 + x + x^2)) + O(x^100)) \\ Colin Barker, Oct 10 2019

CROSSREFS

Cf. A057446, A057216, A057522, A057534, A057614. See also A033478, A057688, A057684, A057685, A057686, A057687, A057689, A057690, A057691.

Cf. A259207.

Sequence in context: A137115 A060063 A106295 * A259207 A300005 A048269

Adjacent sequences:  A057685 A057686 A057687 * A057689 A057690 A057691

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Oct 20 2000

STATUS

approved

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Last modified September 20 10:51 EDT 2021. Contains 347584 sequences. (Running on oeis4.)