login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A297307 Given n, define the sequence x(1) = n, thereafter if x(i) is even set x(i+1) = x(i)/2, if x(i) is odd and divisible by 3, 5 or 7 set x(i+1) = 5*x(i) + 1, otherwise set x(i+1) = 3*x(i) + 1. Then a(n) is the smallest i>1 such that x(i) = 1, 5, or 553, or -1 if none of those numbers is ever reached. 3
4, 2, 6, 3, 7, 7, 22, 4, 19, 2, 10, 8, 5, 23, 19, 5, 8, 20, 16, 3, 9, 11, 17, 9, 39, 6, 12, 24, 14, 20, 78, 6, 36, 9, 15, 21, 27, 17, 34, 4, 81, 10, 39, 12, 55, 18, 76, 10, 31, 40, 10, 7, 7, 13, 46, 25, 32, 15, 28, 21, 21, 79, 37, 7, 37, 37, 23, 10, 43, 16, 74, 22 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

(The following comments needs editing - N. J. A. Sloane, Feb 11 2018)

This is the Syracuse sequence modified by adding a constraint.

if x is odd and divisible by 3 or 5 or 7 then x = 5*x + 1 instead of x = 3x + 1, and x = 3*x + 1 if not divisible by 3 or 5 or 7.

The sequence if x even then x = x/2 and if x odd then x = 5*x + 1 diverge for n even > 12 or n odd > 5.

More than 1/3 of the odd numbers are divisible by 3 or 5 or 7 so this sequence will diverge or if not the Syracuse sequence will converge, it is easy to find that with the constraint added this sequence converges but with different cycles which are function of the n starting point.

There are 3 different cycles to end this sequence with the repetition of the cycle.

The main one is with a cycle of 6 values 5, 26, 13, 40, 20, 10 for 3/4 of the n values.

The second one is the same as the Syracuse sequence 1,4,2 for 21/100 of the n values.

And a third with a cycle of 175 values starting 553, 2766, 1383, 6916 ... for 3.3/100 of the n values.

LINKS

Table of n, a(n) for n=1..72.

EXAMPLE

n = 1, x(1) = 1 , x(2)= 4, x(3) = 2, x(4) = 1 so a(1) = 4.

MATHEMATICA

With[{a = {3, 5, 7}, b = {1, 5, 553}, nn = 10^3}, Array[Length@ NestWhileList[Function[n, Which[EvenQ@ n, n/2, And[OddQ@ n, AnyTrue[a, Divisible[n, #] &]], 5 n + 1, True, 3 n + 1]], #, FreeQ[b, #] &, {2, 1}, nn] /. k_ /; k == nn + 1 -> -1 &, 72]] (* Michael De Vlieger, Dec 31 2017 *)

PROG

(BASIC)

For n=1 to 5000

i=1:x=n

10 i=i+1

If x-2*Int(x/2)=0 Then x=x/2:Goto 20

If x-3*Int(x/3)=0 or x-5*Int(x/5)=0 Then x=5*x+1:Goto 20

x=3*x+1

20 if x=1 or x=5 or x=553 Then Print n; i:Goto 30

Goto 10

30 Next n

End

CROSSREFS

Cf. A006577, A297217.

Sequence in context: A246879 A302794 A247361 * A163238 A097362 A129131

Adjacent sequences:  A297304 A297305 A297306 * A297308 A297309 A297310

KEYWORD

nonn

AUTHOR

Pierre CAMI, Dec 28 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 25 16:01 EST 2022. Contains 350572 sequences. (Running on oeis4.)