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A064403 Numbers k such that prime(k) + k and prime(k) - k are both primes. 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Starting with 6 all terms are == 0 (mod 6). - Zak Seidov, Jan 04 2013
LINKS
EXAMPLE
4 is in the sequence because the fourth prime is 7 and both 7+4 and 7-4 are primes.
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Cf. A143794 (corresponding primes).
Sequence in context: A051253 A175955 A303526 * A235344 A060667 A218065
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Sep 28 2001
STATUS
approved

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Last modified July 21 14:09 EDT 2024. Contains 374474 sequences. (Running on oeis4.)