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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).

%I A081413 #29 Mar 11 2025 04:41:45
%S A081413 3,23,139,113,1129,2477,1327,30593,81463,44293,34061,404597,265621,
%T A081413 155921,1100977,1098847,1349533,3117299,6958667,10343761,6034247,
%U A081413 49269581,83751121,39389989,166726367,107534587,232423823,253878403,327966101,519653371,1202442089,1649328997
%N 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).
%F A081413 a(n) = min{ prime(j) : A006530(prime(j+1)-prime(j)) = prime(n) }.
%F A081413 For n > 1, a(n) = A080082(n). - _Zak Seidov_, Jul 05 2013
%t A081413 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 *)
%o A081413 (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
%Y A081413 Cf. A001223, A006530, A080082, A000230, A000040.
%K A081413 nonn
%O A081413 1,1
%A A081413 _Labos Elemer_, Apr 02 2003
%E A081413 Three more terms added from A080082 by _Zak Seidov_, Jul 05 2013
%E A081413 a(22) corrected and a(29)-a(32) added by _Amiram Eldar_, Mar 11 2025