A175867 a(0) = 2; a(n) = a(n - 1) * 2 + 1 if a(n - 1) is prime, or a(n - 1) / (smallest prime factor) if it is composite.

2, 5, 11, 23, 47, 95, 19, 39, 13, 27, 9, 3, 7, 15, 5, 11, 23, 47, 95, 19, 39, 13, 27, 9, 3, 7, 15, 5, 11, 23, 47, 95, 19, 39, 13, 27, 9, 3, 7, 15, 5, 11, 23, 47, 95, 19, 39, 13, 27, 9, 3, 7, 15, 5, 11, 23, 47, 95, 19, 39, 13, 27, 9, 3, 7, 15, 5, 11, 23, 47, 95, 19, 39, 13, 27, 9, 3, 7

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

Table of n, a(n) for n=0..77.

Wikipedia, Divisor

Wikipedia, Prime number

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

Sequence in context: A000100 A293339 A348855 * A083005 A133489 A060153

Adjacent sequences: A175864 A175865 A175866 * A175868 A175869 A175870

Keyword

easy,nonn

Author

Grant Garcia, Sep 30 2010

Status

approved