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Search: id:A100486
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| A100486 |
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a(n) = pi(n) + n-th prime, where pi(n) = A000720(n) is the prime counting function. |
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3
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| 2, 4, 7, 9, 14, 16, 21, 23, 27, 33, 36, 42, 47, 49, 53, 59, 66, 68, 75, 79, 81, 87, 92, 98, 106, 110, 112, 116, 119, 123, 138, 142, 148, 150, 160, 162, 169, 175, 179, 185, 192, 194, 205, 207, 211, 213, 226, 238, 242, 244, 248, 254, 257, 267, 273, 279, 285, 287
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This sequence is asymptotic to Li(n) + n/ln(n). Conjecture: it contains infinitely many primes, beginning with 2, 7, 23, 47, 53, 59, 79, 179, 211, 257.
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REFERENCES
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Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, 1993.
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LINKS
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Andrew Booker, The Nth Prime Page.
Eric Weisstein's World of Mathematics, "Prime Counting Function."
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EXAMPLE
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a(21) = 81 because a(21) = pi(21) + 21st prime = 8 + 73 = 81.
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MATHEMATICA
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Table[PrimePi[n] + Prime[n], {n, 60}]
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CROSSREFS
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Cf. A000720, A065042, A100917.
Adjacent sequences: A100483 A100484 A100485 this_sequence A100487 A100488 A100489
Sequence in context: A139444 A024679 A090893 this_sequence A139533 A039904 A115162
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Nov 22 2004
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