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Search: id:A106350
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| A106350 |
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Semiprimes indexed by primes. |
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+0
15
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| 6, 9, 14, 21, 33, 35, 49, 55, 65, 86, 91, 115, 122, 129, 142, 159, 183, 187, 206, 215, 218, 247, 259, 287, 303, 319, 323, 334, 339, 358, 403, 415, 453, 466, 497, 502, 519, 537, 545, 573, 591, 611, 655, 667, 681, 687, 718, 763, 778, 781, 793, 813, 817, 862, 879
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This is the sequence of the n-th semiprime for n = {2,3,5,7,11,13,17,19,23,29...}. Not to be confused with A106349: Primes indexed by semiprimes. We seek to know what this sequence is asymptotically, as J. B. Rosser's result, subsequently modified, is that prime(n) ~ n*(ln n + ln ln n - 1). hence semiprime(prime(n)) ~ semiprime(n)*(ln semiprime(n) + ln ln semiprime(n) - 1). But what is, asymptotically, semiprime(n)?
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REFERENCES
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Rosser, J. B. "The n-th Prime is Greater than nlog(n)." Proc. London Math. Soc. 45, 21-44, 1938.
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LINKS
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Eric Weisstein's World of Mathematics, Semiprime.
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FORMULA
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a(n) = semiprime(prime(n)). a(n) = A001358(A000040(n)).
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EXAMPLE
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a(1) = semiprime(prime(1)) = semiprime(2) = 6.
a(2) = semiprime(prime(2)) = semiprime(3) = 9.
a(3) = semiprime(prime(3)) = semiprime(5) = 14.
a(4) = semiprime(prime(4)) = semiprime(7) = 21.
a(5) = semiprime(prime(5)) = semiprime(11) = 33.
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CROSSREFS
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Cf. A000040, A001358, A007097, A091022, A105997, A105998, A106349.
Sequence in context: A095098 A134859 A154778 this_sequence A020717 A139322 A139321
Adjacent sequences: A106347 A106348 A106349 this_sequence A106351 A106352 A106353
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 30 2005
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