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Search: id:A103668
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| A103668 |
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Number of semiprimes between prime(n) and prime(n+1). |
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+0
5
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| 0, 1, 1, 2, 0, 2, 0, 2, 2, 0, 3, 2, 0, 1, 2, 3, 0, 2, 1, 0, 2, 1, 3, 4, 0, 0, 1, 0, 1, 6, 1, 2, 0, 5, 0, 1, 3, 1, 1, 2, 0, 3, 0, 1, 0, 6, 7, 1, 0, 0, 2, 0, 2, 2, 2, 2, 0, 1, 1, 0, 3, 7, 1, 0, 1, 6, 2, 3, 0, 0, 2, 3, 1, 1, 2, 1, 4, 1, 2, 4, 0, 2, 0, 1, 0, 3, 3, 1, 0, 1, 4, 3, 1, 2, 2, 1, 5, 0, 7, 3, 3, 2, 2, 0, 1
(list; graph; listen)
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OFFSET
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1,4
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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EXAMPLE
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a(4)=2 because between prime(4)=7 and prime(5)=11 there are two semiprimes: 3*3 and 2*5.
a(11)=3 because between p(11)=31 and p(12)=37 there are three semiprimes: 33=3*11, 34=2*17, and 35=5*7.
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MATHEMATICA
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fQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; f[n_] := Count[fQ /@ Range[Prime[n] + 1, Prime[n + 1] - 1], True]; Table[ f[n], {n, 105}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), May 07 2005)
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CROSSREFS
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The first occurrence of k = 0, 1, 2, ... is at position 1, 2, 4, 11, 24, 34, 30, 47, ... (A103669).
Primes: A000040, semiprimes: A001358, number of primes between two successive semiprimes: A088700.
Cf. A103654, A103655, A103669.
Sequence in context: A029225 A116127 A039979 this_sequence A076472 A140302 A085341
Adjacent sequences: A103665 A103666 A103667 this_sequence A103669 A103670 A103671
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KEYWORD
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base,nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Feb 12 2005
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