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A136014
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Numbers n such that n*(n-1)-1 and n*(n+3)+1 are both prime.
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0
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3, 4, 5, 7, 9, 10, 12, 14, 20, 25, 27, 29, 40, 45, 47, 49, 54, 55, 65, 67, 69, 84, 95, 102, 139, 154, 159, 170, 175, 185, 187, 192, 194, 219, 232, 245, 247, 264, 289, 295, 297, 302, 304, 350, 359, 379, 392, 394, 419, 432, 449, 454, 462, 472, 474, 495, 500
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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EXAMPLE
| 3,s=3+4=7,t=3*4=12,t-s=12-7=5, prime, t+s=12+5=17, prime
4,s=4+5=9,t=4*5=20,t-s=20-9=11, prime,t+s=20+9=29, prime
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MAPLE
| a:=proc(n) local s, t: s:= 2*n+1: t:= n*(n+1): if isprime(t-s)=true and isprime(t+s)=true then n else end if end proc: seq(a(n), n=1..400); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 31 2008
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MATHEMATICA
| a = ""; For[i = 1, i < 10^2, j = i + 1; s = i + j; m = i*j; p1 = m - s; p2 = m + s; If[PrimeQ[p1] && PrimeQ[p2], a = a <> ToString[i] <> ", "]; i++ ]; Print[a <> ".."]
Select[Range[500], PrimeQ[ #*(# - 1) - 1] && PrimeQ[ #*(# + 3) + 1] &] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 24 2008
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CROSSREFS
| Sequence in context: A184419 A189665 A156246 * A112930 A003159 A187691
Adjacent sequences: A136011 A136012 A136013 * A136015 A136016 A136017
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KEYWORD
| nonn
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AUTHOR
| Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 21 2008
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EXTENSIONS
| Edited with more terms by Stefan Steinerberger (stefan.steinerberger(AT)gmail.com) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 24 2008
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