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Search: id:A060646
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| A060646 |
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Bonse sequence: a(n) = minimal j such that n-j+1 < prime(j). |
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3
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| 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 18, 18
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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For 3<n and any a(n-1)<a(n) use a(n)=a(n+1)=a(n+2) to show prime(j+1)^3 < prime(1)*...*prime(j) for j>5.
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REFERENCES
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Bonse, Archiv d. Math. u. Physik (3) vol. 12 (1907) 292-295
Rademacher and Toeplitz, Von Zahlen und Figuren (1930, reprint Springer 1968), ch. 22, "Eine Eigenschaft der Zahl 30" (A property of the number 30).
R. Remak, Archiv d. Math. u. Physik (3) vol. 15 (1908) 186-193
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EXAMPLE
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For n=5, j=3 gives 5-3+1 = 3 < prime(3) = 5, true; but if j=2 we get 5-2+1 = 4 which is not < prime(2) = 3; hence a(5) = 3.
a(75)=18 because 75-18+1=58 < 61=prime(18), but 75-17+1=59=prime(17)
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CROSSREFS
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prime(j) = A000040(j).
Sequence in context: A110867 A006670 A132914 this_sequence A103298 A082429 A047744
Adjacent sequences: A060643 A060644 A060645 this_sequence A060647 A060648 A060649
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KEYWORD
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easy,nonn,nice
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AUTHOR
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Frank Ellermann (Frank.Ellermann(AT)t-online.de), Apr 17 2001
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