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Search: id:A086979
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| 46, 282, 738, 3302, 7970, 8028, 14862, 15783, 34202, 44773, 44903, 85787, 110224, 165326, 402884, 460883, 474029, 786922, 887313, 2959782, 4875380, 8321465, 9330121, 20226285, 45808557, 92276646, 114867712, 201745031, 265878477
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n) is Pi(p_k) the count of the number of primes up to and including p_k, where p_k is the initial prime of a prime gap g = p_k+1 - p_k. All even gaps smaller than g occur at a smaller prime and the next even gap g+2 also occurs earlier.
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REFERENCES
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P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 144.
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LINKS
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T. R. Nicely, List of "First occurrence prime gaps"
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. Prime Gaps.
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EXAMPLE
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282 is in this list because the 282nd prime is 1831, the next prime
is 1847, giving a prime gap of 16. All even gaps less than 16 occur
before this (for smaller primes) and the next even gap, 18, also
occurs earlier.
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CROSSREFS
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Cf. A000230, A001223, A001632, A038664, A086977, A086978, A086980.
Sequence in context: A044759 A083358 A026913 this_sequence A077734 A135735 A111304
Adjacent sequences: A086976 A086977 A086978 this_sequence A086980 A086981 A086982
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KEYWORD
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nonn
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AUTHOR
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Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 26 2003
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