A057688 Trajectory of 5 under the '5x+1' map.

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

Offset: 0

Author

N. J. A. Sloane, Oct 20 2000

Keywords

• nonn
• easy

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

Examples

			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.
		

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,1).

Crossrefs

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

Cf. A259207.

Programs

Mathematica

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

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

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)