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 A091592 Numbers n such that there are no twin primes between n^2 and (n+1)^2. 8
 1, 9, 19, 26, 27, 30, 34, 39, 49, 53, 77, 122 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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. - Arkadiusz Wesolowski, Jul 11 2011 LINKS Table of n, a(n) for n=1..12. A. Kourbatov, Maximal Gaps Between Prime k-Tuples: A Statistical Approach, J. Int. Seq. 16 (2013) #13.5.2 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. EXAMPLE 9 is a term because no twin primes are found in the interval [9^2,10^2]. 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: # R. J. Mathar, Aug 26 2008 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}] CROSSREFS Cf. A091591, A036061, A036063, A113274. Sequence in context: A228610 A106677 A350261 * A174372 A145906 A090065 Adjacent sequences: A091589 A091590 A091591 * A091593 A091594 A091595 KEYWORD nonn,hard,more AUTHOR Hugo Pfoertner, Jan 25 2004 EXTENSIONS Edited by N. J. A. Sloane, Aug 31 2008 at the suggestion of Pierre CAMI STATUS approved

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Last modified October 4 02:45 EDT 2023. Contains 365872 sequences. (Running on oeis4.)