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A064403
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Numbers k such that prime(k) + k and prime(k) - k are both primes.
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10
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4, 6, 18, 42, 66, 144, 282, 384, 408, 450, 522, 564, 618, 672, 720, 732, 744, 828, 858, 1122, 1308, 1374, 1560, 1644, 1698, 1776, 1848, 1920, 2022, 2304, 2412, 2616, 2766, 2778, 2874, 2958, 2970, 3036, 3042, 3240, 3258, 3354, 3360, 3432, 3540, 3594, 3732
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OFFSET
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1,1
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COMMENTS
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Starting with 6 all terms are == 0 (mod 6). - Zak Seidov, Jan 04 2013
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LINKS
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EXAMPLE
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4 is in the sequence because the fourth prime is 7 and both 7+4 and 7-4 are primes.
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MATHEMATICA
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Select[ Range[ 4000 ], PrimeQ[ Prime[ # ] + # ] && PrimeQ[ Prime[ # ] - # ] & ]; Join[{4}, Select[ Range[6, 4000, 6 ], PrimeQ[Prime[ # ] + # ] && PrimeQ[ Prime[ # ] - # ] & ]] (* Zak Seidov, Jan 04 2013 *)
Select[Range[4000], AllTrue[Prime[#]+{#, -#}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 25 2019 *)
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PROG
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(PARI) { n=0; default(primelimit, 1800000); for (m=1, 10^9, if (isprime(prime(m) + m) && isprime(prime(m) - m), write("b064403.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 13 2009
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CROSSREFS
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Cf. A143794 (corresponding primes).
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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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