A177980 Iterate (n + lpf(n)) / 2 until a prime is reached, where lpf equals the least prime factor. a(n) is that terminating prime.

2, 3, 3, 5, 3, 7, 5, 3, 3, 11, 7, 13, 5, 3, 3, 17, 3, 19, 11, 7, 7, 23, 13, 3, 5, 3, 3, 29, 3, 31, 17, 3, 3, 11, 19, 37, 11, 7, 7, 41, 7, 43, 23, 13, 13, 47, 3, 3, 5, 3, 3, 53, 3, 3, 29, 3, 3, 59, 31, 61, 17, 3, 3, 11, 3, 67, 11, 19, 19, 71, 37, 73, 11

Offset: 2

Author

Grant Garcia, Dec 16 2010

Keywords

• nonn

Comments

The function (n + lpf(n)) / 2 reduces the input according to its lowest prime factor if it is composite or simply returns the input if it is prime.

Sequence contains only prime numbers (and every prime number).

Examples

			7 is prime, so (7 + lpf(7)) / 2 = (7 + 7) / 2 = 7.
15 is composite: (15 + 3) / 2 = 9, (9 + 3) / 2 = 6, (6 + 2) / 2 = 4, (4 + 2) / 2 = 3.
		

Links

• Dumitru Damian, Table of n, a(n) for n = 2..30000

Crossrefs

Cf. A020639, A061228.

Programs

Mathematica

g[n_] := (n + FactorInteger[n][[1, 1]])/2; f[n_] := Last@ NestWhileList[g, n, !PrimeQ@ # &]; Array[f, 73, 2]

Python

from sympy import factorint, isprime
def a177980(n):
    while True:
        if isprime(n): return n
        else: n=int((n+A020639(n))/2)
[a177980(n) for n in range(2, 160)] # Dumitru Damian, Dec 15 2021