cp's OEIS Frontend

A214093 Largest prime p such that the greatest prime factor of p^2-1 is prime(n).

%I A214093 #9 Apr 02 2013 17:15:30
%S A214093 3,17,31,4801,881,8191,388961,1419263,4046849,36171409,4620799,
%T A214093 617831551,170918749,842277599279,3554663111,187753824257,19854354911,
%U A214093 1233008445689,60292968751,508070657249,4421151404801,259476225058051,17431549081705001,45163738135361,99913980938200001
%N A214093 Largest prime p such that the greatest prime factor of p^2-1 is prime(n).
%C A214093 The terms were computed using Filip Najman's list, see the link.
%H A214093 Filip Najman, <a href="http://web.math.hr/~fnajman/">Home Page</a> (gives all numbers n such that n^2-1 has no prime factor greater than 97)
%e A214093 a(6)=8191 because 8190 = 2*3^2*5*7*13, 8192=2^13 and prime(6)=13.
%o A214093 (PARI)
%o A214093 /* up to term for p=97 */
%o A214093 /* S[] is the list computed by Filip Najman (16223 elements) */
%o A214093 S=[2, 3, 4, ... , 332110803172167361, 19182937474703818751];
%o A214093 lpf(n)={ vecmax(factor(n)[, 1]) } /* largest prime factor */
%o A214093 { forprime (p=2, 97,
%o A214093   t = 0;
%o A214093   for (n=1,#S, if ( lpf(S[n]^2-1)==p && isprime(S[n]), t=n ); );
%o A214093   print1(S[t],", ");
%o A214093 );}
%Y A214093 Cf. A175607 (largest number k such that the greatest prime factor of k^2-1 is prime(n)).
%K A214093 nonn,hard
%O A214093 1,1
%A A214093 _Joerg Arndt_, Jul 03 2012