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Primes for which the weight as defined in A117078 is 7 and the gap as defined in A001223 is 4.
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%I #7 Sep 17 2022 09:43:01

%S 67,193,277,487,613,823,907,1663,1873,2083,2293,2377,2797,3217,3343,

%T 3847,4813,5233,5527,5653,5737,6577,6997,7207,7753,8677,8803,9433,

%U 11113,11617

%N Primes for which the weight as defined in A117078 is 7 and the gap as defined in A001223 is 4.

%C The prime numbers in this sequence are of the form (14i-3) with i=(level(n)+1)/2, level(n) defined in A117563.

%H Remi Eismann, <a href="/A119593/b119593.txt">Table of n, a(n) for n=1..10000</a>

%F Primes p such that (1) p = 53 or 67 mod 70 and (2) p+4 is prime. - _Charles R Greathouse IV_, Sep 17 2022

%F a(n) = Omega(n log^2 n). - _Charles R Greathouse IV_, Sep 17 2022

%o (PARI) forprimestep(p=67,1e4,14, t=p%5; if((t==2 || t==3) && isprime(p+4), print1(p", "))) \\ _Charles R Greathouse IV_, Sep 17 2022

%o (PARI) p=67; forprime(q=p+2,1e4, if(q-p==4 && (p%70==53 || p%70==67), print1(p", ")); p=q) \\ _Charles R Greathouse IV_, Sep 17 2022

%Y Cf. A117078, A001223, A117563, A001359, A118359, A074822, A118922, A118924, A119504.

%K nonn,easy

%O 1,1

%A _RĂ©mi Eismann_, Jun 01 2006, May 04 2007