A096476 a(n) = prime(A096475(n)).

5, 59, 31, 179, 353, 547, 109, 4133, 6841, 773, 9293, 3733, 10559, 17627, 108643, 9973, 32261, 3259, 22811, 18617, 65731, 60821, 156371, 404029, 55733, 40637, 540619, 192677, 290897, 118297, 693877, 406883, 812527, 264659, 1022303, 928471

Offset

3,1

Comments

Both a(n) and a(n) + 2*n are primes.

a(n) + 2*n is not necessarily the next prime after a(n).

Links

Amiram Eldar, Table of n, a(n) for n = 3..202

Formula

a(n) = A000040(A096475(n)).

Example

a(6) = 179 is a prime and 2*6 + 179 = 12 + 179 = 191 is also a prime, while pi(191) = 43, pi(179) = 41 are twin primes and 179 is the 6th term of A096475 (offset = 3).

Mathematica

{ta=Table[0, {1300}], tb=Table[0, {1300}], tc=Table[0, {1300}], u=1}; Do[s=Prime[n+1]-Prime[n]; If[Equal[s, 2], ta[[u]]=Prime[Prime[n+1]]-Prime[Prime[n]]; tb[[u]]=n; tc[[u]]=Prime[n]; td[[u]]=Prime[Prime[n]]; u=u+1], {n, 1, 10000}]; td

Prog

(PARI) list(len) = {my(v = vector(len), c = 0, q = 2, p1 = 2, p2 = 3, i); forprime(p3 = 5, , q++; if(isprime(q) && isprime(q-2), i = (p3-p1)/2 - 2; if(i <= len && v[i]==0, v[i] = p1; c++; if(c == len, break))); p1 = p2; p2 = p3); v; } \\ Amiram Eldar, Feb 14 2025

Crossrefs

Cf. A000720, A001359, A096474, A096475.

Sequence in context: A336258 A001624 A267722 * A158694 A015994 A222563

Adjacent sequences: A096473 A096474 A096475 * A096477 A096478 A096479

Keyword

nonn

Author

Labos Elemer, Jun 23 2004

Status

approved