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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. 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 19 16:01 EDT 2021. Contains 345144 sequences. (Running on oeis4.)