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A177980
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Iterate (n + lpf(n)) / 2 until a prime is reached, where lpf equals the least prime factor. a(n) is that terminating prime.
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4
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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
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2,1
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COMMENTS
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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).
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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g[n_] := (n + FactorInteger[n][[1, 1]])/2; f[n_] := Last@ NestWhileList[g, n, !PrimeQ@ # &]; Array[f, 73, 2]
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PROG
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(Python)
from sympy import factorint, isprime
def a177980(n):
while True:
if isprime(n): return n
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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