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Search: id:A065857
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| A065857 |
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The (10^n)-th composite number. |
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+0
2
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| 4, 18, 133, 1197, 11374, 110487, 1084605, 10708555, 106091745, 1053422339, 10475688327, 104287176419, 1039019056246, 10358018863853
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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Bojarincev,A.E.:Asymptotic expressions for the n-th composite number.Univ.Mat.Zap. 6:21-43(1967).- In Russian.
Panaitopol, L: Some Properties of the Series of Composed Numbers.J.Inequalities in Pure and Applied Mathematics. 2(2):Article 38, 2000.
J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6: 64-94 (1962).
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LINKS
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J.Inequalities in Pure and Applied Mathematics.
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EXAMPLE
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The 100th composite number is c[100]=133, while the 100th prime is 541>>133=7.19. In general: A000720[m] < A0062298[m] < m < A002808[m] < A000040[m], for m = 100: pi[100]=25 < 75 < m=100 < c[100]=133 < p[100]=541
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MATHEMATICA
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Composite[n_Integer] := Block[ {k = n + PrimePi[n] + 1 }, While[ k != n + PrimePi[k] + 1, k = n + PrimePi[k] + 1]; Return[ k ]]; Table[ Composite[n], {n, 0, 13} ]
composite[n_] := FixedPoint[n+PrimePi[ # ]+1&, n] Table[c[w], {w, 1, 14}]
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CROSSREFS
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Cf. A033844, A002808, A018252, A062298, A000720, A000720, A000040, A006988, A065855, A065856
Adjacent sequences: A065854 A065855 A065856 this_sequence A065858 A065859 A065860
Sequence in context: A108704 A001423 A034517 this_sequence A060841 A059837 A054759
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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), Nov 26 2001
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 26 2001
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