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Search: id:A122933
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| A122933 |
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a(n)-th prime is equal to the sum_{i=1..k} pi(i) for some k (cf. A000720). |
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2
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| 2, 3, 5, 8, 9, 12, 14, 18, 23, 28, 42, 58, 61, 70, 91, 95, 101, 103, 132, 142, 150, 161, 167, 170, 248, 347, 361, 382, 409, 412, 424, 463, 476, 514, 532, 561, 645, 666, 710, 724, 736, 788, 795, 869, 999, 1010, 1083, 1106, 1124, 1136, 1143, 1149, 1163, 1205, 1244
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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A046992 is sum_{k=1..n} pi(k). A122516 are the members of A046992 which are primes.
Primes in A046992[n] are {3,5,11,19,23,37,43,61,...} = A122516[n] = Prime[a(n)].
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FORMULA
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a(n) = PrimePi[ A122516[n] ].
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EXAMPLE
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A122516[n] begins {3,5,11,19,23,37,43,61,83,107,181,271,...}.
So a(1) = 2 because A122516[1] 3 = Prime[2].
a(2) = 3 because A122516[2] = 5 = Prime[3].
a(3) = 5 because A122516[3] = 11 = Prime[5].
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MATHEMATICA
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PrimePi[Flatten[Table[If[PrimeQ[Sum[ PrimePi[n], {n, 1, m}]], Sum[PrimePi[n], {n, 1, m}], {}], {m, 1, 500}]]]
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CROSSREFS
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Cf. A122516, A046992, A000720, A020641.
Sequence in context: A153081 A095952 A025033 this_sequence A091513 A060138 A139487
Adjacent sequences: A122930 A122931 A122932 this_sequence A122934 A122935 A122936
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 20 2006
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EXTENSIONS
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Edited by Robert G. Wilson v Sep 28 2006.
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