A293982 Length (= size) of the orbit of n under iterations of A293975: x -> x/2 if even, x + nextprime(x) if odd; or -1 if the orbit is infinite.

1, 5, 5, 5, 5, 8, 6, 13, 5, 11, 9, 9, 7, 10, 14, 8, 6, 14, 12, 14, 10, 12, 10, 13, 8, 19, 11, 17, 15, 11, 9, 17, 7, 17, 15, 15, 13, 15, 15, 13, 11, 15, 13, 18, 11, 16, 14, 22, 9, 16, 20, 14, 12, 18, 18, 16, 16, 14, 12, 12, 10, 10, 18, 22, 8, 20, 18, 20, 16, 18, 16, 16, 14

Offset: 0

Author

M. F. Hasler, Nov 05 2017

Keywords

• nonn

Comments

The orbit of x under f is O(x; f) = { f^k(x); k = 0, 1, 2,... }.

It is conjectured that for f = A293975, the trajectory (f^k(x); k >= 0) ends in the cycle 1 -> 3 -> 8 -> 4 -> 2 -> 1 for any starting value x.

Examples

			a(0) = 1 = # { 0 }, since 0 -> 0 -> 0 ... under A293975.
a(1) = 5 = # { 1, 3, 8, 4, 2 }, since 1 -> (1 + 2 =) 3 -> (3 + 5 =) 8 -> 4 -> 2 -> 1 -> 3 etc... under A293975.
a(2) = 5 = # { 2, 1, 3, 8, 4 }, since 2 -> 1 -> 3 -> 8 -> 4 -> 2 -> 1 etc... under A293975.
a(5) = 8 = # { 5, 12, 6, 3, 8, 4, 2, 1 }, since 5 -> (5 + 7 =) 12 -> 6 -> 3 -> (3 + 5 =) 8 -> 4 -> 2 -> 1 -> 3 etc... under A293975.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A293975, A174221 (the "PrimeLatz" map), A006370 (the "3x+1" map).

Programs

Mathematica

Table[Flatten[FindTransientRepeat[NestList[If[EvenQ[#],#/2,#+ NextPrime[ #]]&,n,100],3]]//Length,{n,0,80}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 13 2018 *)

PARI

A293982(n,S=[n])={while(#S<#S=setunion(S,[n=A293975(n)]),);#S}