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A001632
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Smallest prime p such that there is a gap of 2n between p and previous prime.
(Formerly M3812 N1560)
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13
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5, 11, 29, 97, 149, 211, 127, 1847, 541, 907, 1151, 1693, 2503, 2999, 4327, 5623, 1361, 9587, 30631, 19373, 16183, 15727, 81509, 28277, 31957, 19661, 35671, 82129, 44351, 43391, 34123, 89753, 162209, 134581, 173429, 31469, 404671, 212777
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OFFSET
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1,1
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COMMENTS
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Smallest prime preceded by 2n-1 successive composites. - Lekraj Beedassy, Apr 23 2010
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REFERENCES
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J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 97, p. 34, Ellipses, Paris 2008.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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EXAMPLE
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The first time a gap of 4 occurs between primes is between 7 and 11, so A000230(2)=7 and A001632(2)=11.
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MATHEMATICA
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With[{pr=Partition[Prime[Range[35000]], 2, 1]}, Transpose[ Flatten[ Table[ Select[pr, #[[2]]-#[[1]]==2n&, 1], {n, 40}], 1]][[2]]] (* Harvey P. Dale, Apr 20 2012 *)
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PROG
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(PARI) LIMIT=10^9; a=[]; i=2; o=2; g=0; forprime(p=3, LIMIT, bittest(g, -o+o=p) && next; a=concat(a, [[p, p-precprime(p-1)]]); g+=1<<a[#a][2]; a=vecsort(a, 2); while(#a>=i && a[i][2]<2*i, print1(a[i][1]", "); i++)) \\ a[1] = [3, 1] is not printed, cf. A000230(0). Limit 10^7 yields a(1), ..., a(70) in 0.3 sec @ 2.5 GHz. \\ M. F. Hasler, Jan 13 2011, updated Jan 26 2015.
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Nov 28 2000 and from Labos Elemer, Nov 29 2000
Terms a(1)-a(146) checked with the PARI program by M. F. Hasler, Jan 13 2011, Jan 26 2015
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STATUS
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approved
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