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Search: id:A113971
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| A113971 |
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Number of semiprimes from n to (4/3)*n. |
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+0
1
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| 0, 0, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 3, 4, 4, 3, 2, 2, 3, 3, 3, 3, 4, 5, 5, 5, 5, 4, 4, 3, 4, 4, 4, 3, 3, 4, 5, 6, 6, 5, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5
(list; graph; listen)
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OFFSET
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1,8
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COMMENT
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a(n) > 0 for all n > 2. a(n) > 1 for all n > 16. This is a semiprime (A001358) related sequence similar to the prime related Bertrand's postulate [1845] that, for n > 1, there is always at least one prime p such that n < p < 2*n. A060715 is the number of primes between n and 2n. A077463 is the number of primes between n and 2n-2.
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LINKS
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Eric Weisstein et al., Bertrand's Postulate.
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FORMULA
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a(n) = card{S such that S is an element of A001358 and n =< S =< 4*n/3}.
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EXAMPLE
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a(1) = 0 because there is no semiprime from 1 through 4/3 = 1.3333...
a(2) = 0 because there is no semiprime from 2 through 8/3 = 2.6666...
a(3) = 1 because there is the semiprime 4 from 3 through 12/3 = 4.
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CROSSREFS
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Cf. A001358, A060715, A077463.
Sequence in context: A116452 A103958 A122923 this_sequence A109338 A071202 A102715
Adjacent sequences: A113968 A113969 A113970 this_sequence A113972 A113973 A113974
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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), Jan 31 2006
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