A279765 Primes p such that p+24 and p+48 are also primes.

5, 13, 19, 23, 59, 79, 83, 89, 103, 149, 233, 269, 283, 349, 373, 409, 419, 439, 443, 499, 523, 569, 593, 653, 709, 773, 829, 839, 859, 863, 929, 1039, 1069, 1259, 1279, 1399, 1423, 1559, 1699, 1753, 1823, 1949, 1979, 2039, 2063, 2089, 2113, 2309, 2333, 2393

Offset

1,1

Comments

Subsequence of A033560. The triples have the form (p,p+d,p+2d). The current sequence (d=24) continues A023241 (d=6), A185022 (d=12) and A156109 (d=18). The frequencies of such triples and the triple (p, p+3±1, p+6) in A007529 do not differ very much (see table in the link "comparison of triples"). For creating the b-file I used a file of prime differences, divided by 2 (extension of A028334). For filling the table I analyzed primes up to 10^9.

Annotation: The algorithm using a file of primes or prime differences is not difficult but not as easy as using a function like isprime(n). On the other hand, such a function needs computing time which is not negligible for large numbers.

Links

Gerhard Kirchner, Table of n, a(n) for n = 1..10000

Gerhard Kirchner, Comparison of triples

Example

First term: 5, 5 + 24 = 29 and 5 + 48 = 53 are all primes.

Mathematica

Select[Prime@Range@500, PrimeQ[# + 24] && PrimeQ[# + 48] &] (* Robert G. Wilson v, Dec 18 2016 *)

Prog

(PARI) is(n) = for(k=0, 2, if(!ispseudoprime(n+24*k), return(0))); 1 \\ Felix Fröhlich, Dec 26 2016

Crossrefs

Cf. A023241, A033560, A156109, A185022.

Sequence in context: A118915 A084442 A023270 * A308196 A287615 A129919

Adjacent sequences: A279762 A279763 A279764 * A279766 A279767 A279768

Keyword

nonn

Author

Gerhard Kirchner, Dec 18 2016

Status

approved