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 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. 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

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Last modified January 21 01:15 EST 2021. Contains 340332 sequences. (Running on oeis4.)