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A088498
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Numbers k such that k^2 + k - 1 and k^2 + k + 1 are twin primes and (k + 1)*(k + 1) + k + 1 - 1 and (k + 1)*(k + 1) + k + 1 + 1 are also twin primes.
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1
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2, 5, 20, 455, 1364, 2204, 2450, 2729, 8540, 18485, 32198, 32318, 32780, 45863, 61214, 72554, 72560, 82145, 83258, 86603, 91370, 95198, 125333, 149330, 176888, 182909, 185534, 210845, 225665, 226253, 288419, 343160, 350090, 403940, 411500
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OFFSET
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1,1
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LINKS
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EXAMPLE
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20 is a term since 20^2 + 20 - 1 = 419, 419 and 421 are twin primes, 21^2 + 21 - 1 = 461, and 461 and 463 are also twin primes.
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MATHEMATICA
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Select[ Range[510397], PrimeQ[ #^2 + # - 1] && PrimeQ[ #^2 + # + 1] && PrimeQ[ #^2 + 3# + 1] && PrimeQ[ #^2 + 3# + 3] & ]
Select[Range[412000], AllTrue[Flatten[{#^2+#+{1, -1}, (#+1)(#+1)+#+{0, 2}}], PrimeQ]&] (* Harvey P. Dale, Feb 12 2022 *)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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