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Search: id:A020497
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| A020497 |
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a(n) is the minimal y such that n primes occur infinitely often among (x+1, ..., x+y), i.e. pi(x+y)-pi(x) >= n for infinitely many x. |
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+0
8
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| 1, 3, 7, 9, 13, 17, 21, 27, 31, 33, 37, 43, 49, 51, 57, 61, 67, 71, 77, 81, 85, 91, 95, 101, 111, 115, 121, 127, 131, 137, 141, 147, 153, 157, 159, 163, 169, 177, 183, 187, 189, 197, 201, 211, 213, 217, 227, 237, 241, 247, 253, 255, 265, 271, 273, 279, 283, 289, 301, 305
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A020497(n) purportedly gives the least k with c(k) = n, where c()=A023193; that is, A020497 should be the "least inverse" of A023193.
My web page extends the sequence to rho(305)=2047 and also gives a super-dense occurrence at rho(592)=4333 when pi(4333)=591 - the first known occurrence. - Thomas J Engelsma (tom(AT)opertech.com), Feb 16 2004
Tomas Oliveira e Silva (see link) has a table extending to n = 1000.
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, (2nd edition, Springer, 1994), Section A9.
H. Smith, "On a generalization of the prime pair problem", Math. Comp., 11 (1957) 249-254.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..672 (from Engelsma's data)
Thomas J. Engelsma, Permissible Patterns.
T. Forbes, Prime k-tuplets
Tomas Oliveira e Silva, Admissible prime constellations
Eric Weisstein's World of Mathematics, Prime k-Tuples Conjecture.
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CROSSREFS
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Equals A008407 + 1. First differences give A047947.
Cf. A023193 (prime k-tuplet conjectures), A066081 (weaker binary conjectures).
Adjacent sequences: A020494 A020495 A020496 this_sequence A020498 A020499 A020500
Sequence in context: A063204 A130568 A143803 this_sequence A023490 A032375 A089556
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KEYWORD
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nonn,nice
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), cet1(AT)cus.cam.ac.uk (Chris Thompson)
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EXTENSIONS
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Corrected and extended by David W. Wilson (davidwwilson(AT)comcast.net).
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