A119593 Primes for which the weight as defined in A117078 is 7 and the gap as defined in A001223 is 4.

67, 193, 277, 487, 613, 823, 907, 1663, 1873, 2083, 2293, 2377, 2797, 3217, 3343, 3847, 4813, 5233, 5527, 5653, 5737, 6577, 6997, 7207, 7753, 8677, 8803, 9433, 11113, 11617

Offset: 1

Author

Rémi Eismann, Jun 01 2006, May 04 2007

Keywords

• nonn
• easy

Comments

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

Links

• Remi Eismann, Table of n, a(n) for n=1..10000

Crossrefs

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

Programs

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

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

Formula

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

a(n) = Omega(n log^2 n). - Charles R Greathouse IV, Sep 17 2022