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Search: id:A073425
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| A073425 |
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a(0)=0; for n>0, a(n) = number of primes not exceeding n-th composite number. |
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+0
12
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| 0, 2, 3, 4, 4, 4, 5, 6, 6, 6, 7, 8, 8, 8, 9, 9, 9, 9, 9, 10, 11, 11, 11, 11, 11, 12, 12, 12, 13, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 18, 18, 18, 18, 18, 19, 19, 19, 20, 21, 21, 21, 21, 21, 22, 22, 22, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 24, 25, 25, 25, 26
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n-1) = A018252(n) - n. a(n-1) = inverse (frequency distribution) sequence of A014689(n), i.e. number of terms of sequence A014689(n) less than n. a(n) = A073169(n+1) - 1, for n >= 1. For n >= 1: a(n) + 1 = A073169(n) = the number of set {1, primes}, i.e. (A158611) less than (n)-th composite numbers (A002828(n)). a(n-1) = The number of primes (A000040(n)) less than n-th nonprime (A018252(n)). - Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Jun 27 2009
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FORMULA
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a(n)=A000720[A002808(n)]
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EXAMPLE
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n=100: composite[100]=133,Pi[133]=32=a(100)
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MATHEMATICA
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c[x_] := FixedPoint[x+PrimePi[ # ]+1&, x] Table[PrimePi[c[w]], {w, 1, 128}]
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CROSSREFS
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Cf. A065890, A073426, A000720, A002808.
Cf. A000040, A018252, A158611, A073169.
Sequence in context: A060740 A145339 A123273 this_sequence A087876 A006158 A135414
Adjacent sequences: A073422 A073423 A073424 this_sequence A073426 A073427 A073428
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jul 31 2002
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EXTENSIONS
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Edited by N. J. A. Sloane, Jul 04 2009 at the suggestion of R. J. Mathar
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