A064403 Numbers k such that prime(k) + k and prime(k) - k are both primes.

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

Offset

1,1

Comments

Starting with 6 all terms are == 0 (mod 6). - Zak Seidov, Jan 04 2013

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

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

Adjacent sequences: A064400 A064401 A064402 * A064404 A064405 A064406

Keyword

nonn

Author

Robert G. Wilson v, Sep 28 2001

Status

approved