A177980 - OEIS

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

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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

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

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

Cf. A020639, A061228.

Sequence in context: A333496 A152864 A152984 * A215405 A064921 A064917

Adjacent sequences: A177977 A177978 A177979 * A177981 A177982 A177983

KEYWORD

nonn

AUTHOR

Grant Garcia, Dec 16 2010

STATUS

approved