

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
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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

Table of n, a(n) for n=0..87.


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.


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 *)


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


AUTHOR

N. J. A. Sloane, Oct 20 2000


STATUS

approved



