A062576 Numbers k such that 10^k - 9^k is prime.

2, 3, 7, 11, 19, 29, 401, 709, 2531, 15787, 66949, 282493

Offset: 1

Author

Mike Oakes, May 18 2001, May 19 2001

Keywords

• nonn
• hard

Comments

Terms > 1000 are often only strong pseudoprimes.

All terms are prime. - Alexander Adamchuk, Apr 27 2008

Examples

			10^2 - 9^2 = 100 - 81 = 19, which is prime, hence 2 is in the sequence.
10^3 - 9^3 = 1000 - 729 = 271, which is prime, hence 3 is in the sequence.
10^4 - 9^4 = 10000 - 6561 = 3439 = 19 * 181, which is not prime, hence 4 is not in the sequence.
		

Links

• Henri & Renaud Lifchitz, PRP Records.

Crossrefs

Cf. A000043, A057468, A059801, A059802, A059803 (9^n-8^n is prime), A062572-A062666.

Cf. A016189 = 10^n - 9^n, and A199819 (primes of this form).

Programs

Mathematica

Select[Range[1000], PrimeQ[10^# - 9^#] &] (* Alonso del Arte, Sep 06 2013 *)

PARI

is(n)=ispseudoprime(10^n-9^n) \\ Charles R Greathouse IV, Feb 20 2017

Extensions

Three more terms 15787, 66949 and 282493 found by Jean-Louis Charton in 2004 and 2007