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Search: id:A113728
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| A113728 |
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a(n) is the integer between p(n) and p(n+2) which is divisible by (p(n+2)-p(n)), where p(n) is the n-th prime. |
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2
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| 3, 4, 6, 12, 12, 18, 18, 20, 24, 32, 40, 42, 42, 50, 48, 56, 64, 70, 72, 72, 80, 80, 84, 96, 102, 102, 108, 108, 126, 126, 130, 136, 144, 144, 152, 156, 160, 170, 168, 176, 180, 192, 192, 198, 210, 216, 224, 228, 228, 230, 240, 240, 256, 252, 264, 264, 272, 280
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Exactly one integer exists between each p(n+2) and p(n) which is divisible by (p(n+2)-p(n)).
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FORMULA
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a(n)=A031131(n)*ceil[A000040(n)/A031131(n)]. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 31 2007
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EXAMPLE
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Between the primes 19 and 29 is the composite 20, and 20 is divisible by (29-19)=10. So 20 is in the sequence.
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MATHEMATICA
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For[n = 1, n < 50, n++, s := Prime[n] + 1; While[Floor[s/(Prime[n + 2] -Prime[n])] != s/(Prime[n + 2] - Prime[n]), s++ ]; Print[s]] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Feb 10 2006
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CROSSREFS
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Cf. A113709, A113729.
Sequence in context: A048229 A002090 A062822 this_sequence A000114 A136243 A051592
Adjacent sequences: A113725 A113726 A113727 this_sequence A113729 A113730 A113731
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Nov 08 2005
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Feb 10 2006
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 31 2007
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