A185396 Largest number x such that the greatest prime factor of x^2-2 is A038873(n), the n-th prime not congruent to 3 or 5 mod 8.

2, 10, 108, 235, 1201, 390050, 314766, 4035, 364384, 50411, 25955045, 5254864, 236558593, 16958526, 20388056, 177544434, 492981885, 2275400230, 256347346, 384902923486, 324850200677887

Offset: 1

Author

Charles R Greathouse IV, Feb 21 2011

Keywords

• nonn

Comments

For any prime p, there are finitely many x such that x^2-2 has p as its largest prime factor.

Links

• Filip Najman, Smooth values of some quadratic polynomials, Glasnik Matematicki Series III 45 (2010), pp. 347-355.
• Filip Najman, Home Page (gives all 537 numbers x such that x^2-2 has no prime factor greater than 199)

Crossrefs

Cf. A242488, A379348.

Equivalents for other polynomials: A175607 (x^2 - 1), A145606 (x^2 + x), A185389 (x^2 + 1).

Extensions

a(21) added by Andrew Howroyd, Dec 22 2024