OFFSET

0,1

COMMENTS

a(n) repeats itself after 14 iterations. Peak is a(5) = 95.

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

LINKS

EXAMPLE

a(0) = 2

a(1) = 2 * 2 + 1 = 5, because a(0) was prime.

a(2) = 5 * 2 + 1 = 11, because a(1) was prime.

...

a(6) = 95 / 5 = 19, because the smallest prime factor of a(5) was 5.

MATHEMATICA

NestList[If[PrimeQ[#], 2#+1, #/FactorInteger[#][[1, 1]]]&, 2, 80] (* or *) PadRight[{2}, 80, {15, 5, 11, 23, 47, 95, 19, 39, 13, 27, 9, 3, 7}] (* Harvey P. Dale, Jun 14 2020 *)

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] * 2 + 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

KEYWORD

easy,nonn

AUTHOR

Grant Garcia, Sep 30 2010

STATUS

approved