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Search: id:A082512
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| A082512 |
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a(n)=p is the smallest prime introducing a consecutive prime-difference pattern as follows: [2,2n,2], i.e. [p,p+2,p+2+2n,p+2+2n+2] are consecutive primes. Increasing middle prime gap in immediate the neighborhood of two small gaps[=2]; a(n)=0 if no such pattern exists. |
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1
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| 0, 5, 0, 0, 137, 0, 0, 1931, 0, 0, 9437, 0, 0, 2969, 0, 0, 20441, 0, 0, 62987, 0, 0, 510401, 0, 0, 48677, 0, 0, 677471, 0, 0, 997811, 0, 0, 173357, 0, 0, 1134311, 0, 0, 3063287, 0, 0, 3591191, 0, 0, 4876511, 0, 0, 838249
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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It is conjectured that twin primes in neighborhood can be separated by arbitrary large gap.
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EXAMPLE
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a(4)=0 because no p can begin a [2,8,2] gap-pattern since Mod[p,6]=5 must hold and following 3 primes give Mod[6] 1,3,5 residues so p+2+8 is not prime; a(n)=0 if 2n congruent 0 or 2 mod 6; a(n) has solution for n=6k+4;
n=16: the 4 corresponding primes and 3 differences are {1931[2]1933[16]1949[2]1951}.
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MATHEMATICA
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d[x_] := Prime[x+1]-Prime[x]; h={k1=2, k2=82, k3=2}; de=Apply[Plus, h]; k=0; Do[If[Equal[d[n], k1]&&Equal[d[n+1], k2]&&Equal[d[n+2], k3], k=k+1; Print[k, n, h, {Prime[n], Prime[n+1], Prime[n+2], Prime[n+3]}]], {n, 1, 10000000}]
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CROSSREFS
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Sequence in context: A075534 A083527 A113038 this_sequence A068385 A071086 A060338
Adjacent sequences: A082509 A082510 A082511 this_sequence A082513 A082514 A082515
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Apr 29 2003
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EXTENSIONS
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Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 15 2006
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