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A095117
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a(n) = pi(n) + n, where pi(n) = A000720(n) is the number of primes <= n.
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18
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0, 1, 3, 5, 6, 8, 9, 11, 12, 13, 14, 16, 17, 19, 20, 21, 22, 24, 25, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 39, 40, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 54, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 76, 77, 79, 80, 81, 82, 83, 84, 86, 87, 88, 89, 91
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OFFSET
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0,3
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COMMENTS
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There exists at least one prime number p such that n < p <= a(n) for n >= 2. For example, 2 is in (2, 3], 5 in (3, 5], 5 in (4, 6], ..., and primes 73, 79, 83 and 89 are in (71, 91] (see Corollary 1 in the paper by Ya-Ping Lu attached in the links section). - Ya-Ping Lu, Feb 21 2021
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LINKS
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FORMULA
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MAPLE
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MATHEMATICA
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PROG
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(Haskell)
(Python)
from sympy import primepi
def a(n): return primepi(n) + n
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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