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

Author

Gerhard Kirchner, Dec 18 2016

Keywords

• nonn

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.

Examples

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

Links

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

Crossrefs

Cf. A023241, A033560, A156109, A185022.

Programs

Mathematica

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

PARI

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