A062619 Numbers k such that 53^k - 52^k is a prime.

3, 19, 29, 37, 1879, 3181, 3331, 19597, 38993, 84239, 90679

Offset: 1

Author

Mike Oakes, May 18 2001, May 19 2001

Keywords

• nonn
• hard

Comments

Terms greater than 1000 often correspond only to strong pseudoprimes. [Clarified by M. F. Hasler, Sep 15 2013]

All terms are prime. - Robert Price, Jan 20 2013

a(12) > 10^5. - Robert Price, Jan 20 2013

To elaborate on Robert Price's comment that all terms are prime: This is also true for all other sequences of numbers n such that k^n - (k-1)^n is prime. It is easy to prove by elementary means that if n = a * b, then k^n - (k-1)^n is divisible by k^(n-a) - (k-1)^(n-a) and k^(n-b) - (k-1)^(n-b). - Alonso del Arte, Sep 15 2013

Crossrefs

Cf. A000043, A057468, A059801, A059802, A062572-A062666.

Extensions

a(8)-a(11) from Robert Price, Jan 20 2013