A080082 Smallest prime p such that there is a gap of 2*prime(n) between p and next prime.

7, 23, 139, 113, 1129, 2477, 1327, 30593, 81463, 44293, 34061, 404597, 265621, 155921, 1100977, 1098847, 1349533, 3117299, 6958667, 10343761, 6034247, 49269581, 83751121, 39389989, 166726367, 107534587, 232423823, 253878403, 327966101, 519653371, 1202442089, 1649328997

Offset: 1

Author

Reinhard Zumkeller, Jan 26 2003

Keywords

• nonn

Crossrefs

Cf. A000040, A000230, A080083.

Programs

PARI

list(len) = {my(v = vector(len), prv = 3, c = 0, d, i); forprime(p = 5, , d = (p - prv)/2; if(isprime(d), i = primepi(d); if(i < = len && v[i] == 0, c++; v[i] = prv; if(c == len, break))); prv = p); v; } \\ Amiram Eldar, Mar 11 2025

Formula

A000230(A000040(n)) < a(n).

a(n) = A080083(n) - 2*A000040(n).

Extensions

a(17)-a(28) from Donovan Johnson, May 30 2010

a(29)-a(32) from Amiram Eldar, Mar 11 2025