

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.


3



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
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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



