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

0,2

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.

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A105444 A240233 A033299 * A071577 A003870 A304681

Adjacent sequences: A293979 A293980 A293981 * A293983 A293984 A293985

Keyword

nonn

Author

M. F. Hasler, Nov 05 2017

Status

approved