A081413 a(n) is the smallest prime p such that the largest prime divisor of the difference nextprime(p) - p equals the n-th prime, prime(n).

3, 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

Labos Elemer, Apr 02 2003

Keywords

• nonn

Crossrefs

Cf. A001223, A006530, A080082, A000230, A000040.

Programs

Mathematica

t=Table[0, {100}]; ma[n_]:=FactorInteger[n][[-1,1]];Do[s=ma[Prime[n+1]-Prime[n]]; If[s<101&&t[[PrimePi[s]]]==0, t[[PrimePi[s]]]=Prime[n]], {n, 2, 170000000}]; t (* Typo fixed by Zak Seidov, Jul 06 2013 *)

PARI

list(len) = {my(v = vector(len), prv = 3, c = 0, d, f, i); forprime(p = 5, , d = p - prv; f = factor(d); i = primepi(f[#f~, 1]); if(i < = len && v[i] == 0, c++; v[i] = prv; if(c == len, break)); prv = p); v;} \\ Amiram Eldar, Mar 11 2025

Formula

a(n) = min{ prime(j) : A006530(prime(j+1)-prime(j)) = prime(n) }.

For n > 1, a(n) = A080082(n). - Zak Seidov, Jul 05 2013

Extensions

Three more terms added from A080082 by Zak Seidov, Jul 05 2013

a(22) corrected and a(29)-a(32) added by Amiram Eldar, Mar 11 2025