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

1,1

Links

M. F. Hasler, Table of n, a(n) for n = 1..128, Nov 21 2025

Formula

a(n) = A000230(A000040(n)). [Corrected by M. F. Hasler, Nov 21 2025]

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

Mathematica

a[n_]:=Module[{p=2}, Until[NextPrime[p]-p==2Prime[n], p=NextPrime[p]]; p]; Array[a, 20] (* James C. McMahon, Nov 26 2025 *)

Prog

(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
(PARI) A080082(n)=A000230(prime(n)) \\ M. F. Hasler, Nov 21 2025

Crossrefs

Cf. A000040, A000230, A080083.

Sequence in context: A064638 A082021 A227254 * A158954 A056205 A099051

Adjacent sequences: A080079 A080080 A080081 * A080083 A080084 A080085

Keyword

nonn

Author

Reinhard Zumkeller, Jan 26 2003

Extensions

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

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

Status

approved