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A091592
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Numbers n such that there are no twin primes between n^2 and (n+1)^2.
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6
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1, 9, 19, 26, 27, 30, 34, 39, 49, 53, 77, 122
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Numbers n such that there is no pair of twin primes P, P+2 with n^2 < P < P+2 < n^2+2*n.
The first 7 terms of this sequence were given by Ernst Jung in a discussion in the Newsgroup de.sci.mathematik entitled "Primzahlen zwischen (2x-1)^2 und (2x+1)^2" (primes between ...and...) with other significant contributions from Hermann Kremer and Rainer Rosenthal. It is conjectured that there are no further terms beyond a(11)=122. This has been tested to 50000 by Robert G. Wilson v.
Tested up to 10^7 and found no such numbers. [From Arkadiusz Wesolowski, Jul 11 2011]
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LINKS
| Hugo Pfoertner, Illustration of record gaps between pairs of twin primes.
Eric Weisstein's World of Mathematics, k-Tuple Conjecture.
Eric Weisstein's World of Mathematics, Twin Prime Conjecture.
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EXAMPLE
| a(1)=9 because no twin primes are found in the interval [9^2,10^2].
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MAPLE
| isA091592 := proc(n) local p; p := nextprime(n^2) ; q := nextprime(p) ; while q < n^2+2*n do if q-p = 2 then RETURN(false) ; fi; p :=q ; q := nextprime(p) ; od: RETURN(true) ; end: for n from 1 do if isA091592(n) then printf("%d ", n) ; fi; od: [From R. J. Mathar, Aug 26 2008]
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MATHEMATICA
| fQ[n_] := StringCount[ ToString@ PrimeQ[ Range[n^2, (n + 1)^2]], "True, False, True"] == 0; lst = {}; Do[ If[ fQ@n, AppendTo[lst, n]], {n, 25000}]
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CROSSREFS
| Cf. A091591, A036061, A036063.
Sequence in context: A079368 A167529 A106677 * A174372 A145906 A090065
Adjacent sequences: A091589 A091590 A091591 * A091593 A091594 A091595
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KEYWORD
| hard,nonn
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AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), Jan 25 2004
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 31 2008 at the suggestion of Pierre CAMI
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