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Search: id:A136015
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| A136015 |
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Prime numbers n such that 2*n+1, n*(n+1)-1 and n*(n+1)+1 are also prime. |
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| 2, 3, 5, 41, 89, 131, 743, 761, 3449, 6173, 9059, 10781, 11549, 13553, 14939, 15569, 16301, 27809, 33479, 54773, 55439, 57149, 70901, 71849, 76091, 97523, 103391, 103643, 104369, 110543, 114269, 115499, 140111, 141539, 153509, 161033, 162251
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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3: prime
3+4=7 prime
3*4=12, 12-1=11 prime, 12+1=13 prime, twin primes
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MAPLE
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a:=proc(n) if isprime(n)=true and isprime(2*n+1)=true and isprime(n*(n+1)-1)= true and isprime(n*(n+1)+1)=true then n else end if end proc: seq(a(n), n=1.. 150000); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2008
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MATHEMATICA
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a = ""; For[i = 1, i < 10^5, j = i + 1; s = i + j; m = i*j; p1 = m - 1; p2 = m + 1; If[PrimeQ[i] && PrimeQ[s] && PrimeQ[p1] && PrimeQ[p2], a = a <> ToString[i] <> ", "]; i++ ]; Print[a <> ".."]
Select[Prime[Range[100000]], PrimeQ[2# + 1] && PrimeQ[ #*(# + 1) - 1] && PrimeQ[ #*(# + 1) + 1] &] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 24 2008
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CROSSREFS
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Adjacent sequences: A136012 A136013 A136014 this_sequence A136016 A136017 A136018
Sequence in context: A041443 A057775 A088483 this_sequence A106713 A106820 A042469
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KEYWORD
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nonn
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AUTHOR
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Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 21 2008
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EXTENSIONS
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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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