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A240133
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Least number k such that n!/k + 1 and n!/k - 1 are twin primes.
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1
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1, 2, 2, 3, 12, 12, 48, 8, 5, 54, 44, 6, 24, 39, 6, 81, 20, 30, 19, 25, 380, 28, 264, 50, 52, 250, 35, 385, 20, 77, 182, 405, 77, 605, 143, 720, 144, 722, 96, 713, 46, 403, 98, 4508, 90, 77, 560, 806, 64, 665, 2376, 1785, 893, 1235, 4278, 159, 66, 1326, 1806, 429, 475
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OFFSET
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3,2
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LINKS
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EXAMPLE
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6!/1-1 (719) and 6!/1+1 (721) are not both prime. 6!/2-1 (359) and 6!/2+1 (361) are not both prime. 6!/3-1 (239) and 6!/3+1 (241) are both prime. thus, a(6) = 3.
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MATHEMATICA
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lnk[n_]:=Module[{nf=n!, k=1}, While[!AllTrue[nf/k+{1, -1}, PrimeQ], k++]; k]; Array[lnk, 70, 3] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 18 2015 *)
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PROG
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(PARI) f(n)=for(k=1, n!, if(floor(n!/k-1)==n!/k-1 && floor(n!/k+1)==n!/k+1, if(ispseudoprime(n!/k-1) && ispseudoprime(n!/k+1), return(k))))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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