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A177980
Iterate (n + lpf(n)) / 2 until a prime is reached, where lpf equals the least prime factor. a(n) is that terminating prime.
4
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
2,1
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).
LINKS
EXAMPLE
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.
MATHEMATICA
g[n_] := (n + FactorInteger[n][[1, 1]])/2; f[n_] := Last@ NestWhileList[g, n, !PrimeQ@ # &]; Array[f, 73, 2]
PROG
(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
CROSSREFS
Sequence in context: A333496 A152864 A152984 * A215405 A064921 A064917
KEYWORD
nonn
AUTHOR
Grant Garcia, Dec 16 2010
STATUS
approved