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%I #16 Dec 26 2016 05:10:01
%S 5,13,19,23,59,79,83,89,103,149,233,269,283,349,373,409,419,439,443,
%T 499,523,569,593,653,709,773,829,839,859,863,929,1039,1069,1259,1279,
%U 1399,1423,1559,1699,1753,1823,1949,1979,2039,2063,2089,2113,2309,2333,2393
%N Primes p such that p+24 and p+48 are also primes.
%C 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.
%C 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.
%H Gerhard Kirchner, <a href="/A279765/b279765.txt">Table of n, a(n) for n = 1..10000</a>
%H Gerhard Kirchner, <a href="/A279765/a279765.pdf">Comparison of triples</a>
%e First term: 5, 5 + 24 = 29 and 5 + 48 = 53 are all primes.
%t Select[Prime@Range@500, PrimeQ[# + 24] && PrimeQ[# + 48] &] (* _Robert G. Wilson v_, Dec 18 2016 *)
%o (PARI) is(n) = for(k=0, 2, if(!ispseudoprime(n+24*k), return(0))); 1 \\ _Felix Fröhlich_, Dec 26 2016
%Y Cf. A023241, A033560, A156109, A185022.
%K nonn
%O 1,1
%A _Gerhard Kirchner_, Dec 18 2016
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