

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
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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



