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!)
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
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.
MATHEMATICA
NestList[If[PrimeQ[#], 3#+1, #/FactorInteger[#][[1, 1]]]&, 2, 80] (* or *) PadRight[{}, 80, {2, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4}] (* Harvey P. Dale, Aug 05 2023 *)
PROG
(Python)
import math
from sympy import isprime
a = [2]
while not a[ -1] in a[:-1]:
if 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
Sequence in context: A076716 A088591 A229493 * A137107 A284921 A174236
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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 06:50 EDT 2024. Contains 370953 sequences. (Running on oeis4.)