

A177980


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


3



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, and simply returns the input if it is prime.
Sequence contains only prime numbers (and every prime number).


LINKS

Table of n, a(n) for n=2..74.


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]


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



