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A110492
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Number of values of k for k=1,2,3,...,n-1, such that n+k divides Prime[n]+Prime[k], where Prime[n] denotes the n-th prime.
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0
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0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 2, 1, 2, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 3, 2, 7, 4, 7, 8, 8, 5, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 1, 2, 1, 1, 0, 1, 1, 0, 1, 2, 1, 2, 1, 4, 1, 2, 1, 3, 3, 4, 5, 1, 5, 4, 8, 0, 0, 0, 0, 0, 0
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OFFSET
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1,5
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COMMENTS
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Surprisingly, the nonzero terms of the sequence seem to occur in well-defined intervals separated by increasingly long intervals of zero terms, with the position of one nonzero interval located at a value of n approximately 2.4 times that of the previous one. See the link for a graph of {a(n)} vs. Log(n) to the base 2.4, for n in {1,2,...,5000}. Further,each of the integer quotients (Prime[n]+ Prime[k])/(n+k) are the same throughout each interval of nonzero values of a(n) and in fact the values of the quotients are precisely the ordinal of that interval of nonzero values.
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LINKS
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Table of n, a(n) for n=1..105.
John W. Layman, View the graph of {a(n)} vs. log(n) to the base 2.4.
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EXAMPLE
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The first five primes are 2,3,5,7,11. We find that 5+1 does not divide 11+2, but 5+2 divides 11+3, 5+3 divides 11+5 and 5+4 divides 11+7. Therefore a(5)=3.
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CROSSREFS
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Sequence in context: A139737 A036113 A199261 * A180995 A144331 A216805
Adjacent sequences: A110489 A110490 A110491 * A110493 A110494 A110495
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KEYWORD
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nonn
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AUTHOR
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John W. Layman, Jul 22 2005
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STATUS
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approved
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