login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A175871 a(0) = 2; a(n) = a(n - 1) * 3 + 1 if a(n - 1) is prime, or a(n - 1) / (smallest prime factor) if it is composite. 2
2, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) repeats itself after 16 iterations. Peak is a(6) = 52.

The function is similar in nature to Collatz's 3x+1 problem, except that it deals with primality instead of parity.

LINKS

Table of n, a(n) for n=0..78.

Wikipedia, Divisor

Wikipedia, Prime number

EXAMPLE

a(0) = 2

a(1) = 2 * 3 + 1 = 7, because a(0) was prime.

a(2) = 7 * 3 + 1 = 22, because a(1) was prime.

a(3) = 22 / 2 = 11, because the smallest prime factor of a(2) was 2.

PROG

(Python) import math, pyecm

# pyecm can be obtained from pyecm.sourceforge.net

a = [2]

while not a[ -1] in a[:-1]:

.if pyecm.isprime(a[ -1]):

..a.append(a[ -1] * 3 + 1)

.else:

..for div in range(2, int(math.sqrt(a[ -1])) + 1):

...if not a[ -1] % div:

....a.append(a[ -1] / div)

....break

print a

CROSSREFS

Cf. A000040, A175867.

Sequence in context: A076716 A088591 A229493 * A137107 A284921 A174236

Adjacent sequences:  A175868 A175869 A175870 * A175872 A175873 A175874

KEYWORD

easy,nonn

AUTHOR

Grant Garcia, Oct 02 2010

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 April 16 18:53 EDT 2021. Contains 343050 sequences. (Running on oeis4.)