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Search: id:A084975
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| A084975 |
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Primes that show the slow decrease in the larger values of the Andrica function Af(k) = sqrt(p(k+1)) - sqrt(p(k)), where p(k) denotes the k-th prime. |
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4
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| 11, 127, 1361, 1693, 2503, 2999, 3299, 4327, 4861, 5623, 31469, 34123, 43391, 44351, 58889, 156007, 370373, 492227, 604171, 1357333, 1562051, 2010881, 2127269, 2238931, 4652507, 6034393, 7230479, 8421403, 8917663, 11114087, 20831533
(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) are the primes p(k+1) such that Af(k) > Af(m) for all m > k. This sequence relies on a heuristic calculation and there is no proof that it is correct.
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REFERENCES
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R. K. Guy, "Unsolved Problems in Number Theory", Springer-Verlag 1994, A8, p. 21.
P. Ribenboim, "The Little Book of Big Primes", Springer-Verlag 1991, p. 143.
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LINKS
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H. J. Smith, Table of n, a(n) for n=1..128
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. Andrica's Conjecture.
H. J. Smith, Andrica's Conjecture
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EXAMPLE
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a(3)=1361 because p(218)=1361, p(217)=1327 and Af(217) = sqrt(1361) - sqrt(1327) = 0.463722... is larger than any value of Af(m) for m>217.
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CROSSREFS
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Cf. A078693, A079098, A079296, A084974, A084976, A084977.
Sequence in context: A088628 A069599 A053546 this_sequence A065543 A015598 A015601
Adjacent sequences: A084972 A084973 A084974 this_sequence A084976 A084977 A084978
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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), Jun 16 2003
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