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A125146
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Primes p such that (p + nextprime + p) and also (p + previousprime + p) are primes.
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3
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5, 13, 17, 103, 197, 227, 787, 823, 911, 919, 1153, 1409, 1487, 1723, 2087, 2647, 2767, 2999, 3001, 3389, 6089, 6781, 6827, 7877, 9463, 10391, 10789, 11117, 11447, 11971, 13523, 13537, 13711, 13807, 14087, 14489, 16063, 18191, 21059, 23371, 25717
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OFFSET
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1,1
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COMMENTS
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First pairs of two successive primes in the sequence are {13, 17}, {911, 919}, {2999, 3001} (twin primes!), {13523, 13537}, {52543, 52553}.
First case of three successive primes is {78059, 78079, 78101}.
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LINKS
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EXAMPLE
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13 is a term because 13 + 17 + 13 = 43 and 13 + 11 + 13 = 37 are primes.
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MAPLE
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Primes:= select(isprime, [2, seq(i, i=3..10^5, 2)]):
Primes[select(t -> isprime(2*Primes[t]+Primes[t-1]) and isprime(2*Primes[t]+Primes[t+1]), [$2..nops(Primes)-1])]; # Robert Israel, Mar 15 2018
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MATHEMATICA
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pQ[n_]:=PrimeQ[2n+NextPrime[n]]&&PrimeQ[2n+NextPrime[n, -1]]; Select[ Prime[Range[2, 3000]], pQ] (* Harvey P. Dale, Apr 25 2011 *)
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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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