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

3, 17, 31, 4801, 881, 8191, 388961, 1419263, 4046849, 36171409, 4620799, 617831551, 170918749, 842277599279, 3554663111, 187753824257, 19854354911, 1233008445689, 60292968751, 508070657249, 4421151404801, 259476225058051, 17431549081705001, 45163738135361, 99913980938200001

Offset: 1

Author

Joerg Arndt, Jul 03 2012

Keywords

• nonn
• hard

Comments

The terms were computed using Filip Najman's list, see the link.

Examples

			a(6)=8191 because 8190 = 2*3^2*5*7*13, 8192=2^13 and prime(6)=13.
		

Links

• Filip Najman, Home Page (gives all numbers n such that n^2-1 has no prime factor greater than 97)

Crossrefs

Cf. A175607 (largest number k such that the greatest prime factor of k^2-1 is prime(n)).

Programs

PARI

/* up to term for p=97 */
/* S[] is the list computed by Filip Najman (16223 elements) */
S=[2, 3, 4, ... , 332110803172167361, 19182937474703818751];
lpf(n)={ vecmax(factor(n)[, 1]) } /* largest prime factor */
{ forprime (p=2, 97,
  t = 0;
  for (n=1,#S, if ( lpf(S[n]^2-1)==p && isprime(S[n]), t=n ); );
  print1(S[t],", ");
);}