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A334614
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a(n) = pi(prime(n) - n) + n, where pi is the prime counting function.
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1
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1, 2, 4, 6, 8, 10, 11, 13, 15, 18, 19, 21, 22, 24, 26, 28, 30, 32, 34, 35, 36, 38, 40, 42, 45, 47, 48, 50, 51, 53, 55, 57, 60, 61, 65, 66, 67, 68, 70, 72, 74, 76, 77, 79, 81, 82, 85, 88, 89, 91, 93, 94, 95, 99, 101, 102, 104, 105, 106, 107, 108, 112, 116, 117
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OFFSET
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1,2
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COMMENTS
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It can be shown that a(n) > a(n-1) >= 1 and a(n) <= 2*n - 1 < 2*n (see proofs in the Links section).
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LINKS
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FORMULA
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MATHEMATICA
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Table[PrimePi[Prime[n] - n] + n, {n, 1, 64}] (* Amiram Eldar, Sep 09 2020 *)
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PROG
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(Python)
from sympy import prime, primepi
for n in range(1, 100001):
a_n = primepi(prime(n) - n) + n
print(a_n)
(PARI) a(n) = n + primepi(prime(n) - n); \\ Michel Marcus, Sep 09 2020
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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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