A068146 Primes of the form a^a - b^b.

3, 23, 229, 3121, 776887, 16774091, 275311670611, 302875106545597, 437893890380859119, 808793517812627212561, 827240252970236315921, 1978419655651397488675723, 20880467999847900922348207352551

Offset: 1

Author

Amarnath Murthy, Feb 23 2002

Keywords

• nonn

Examples

			229 = 4^4 - 3^3 is a prime.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..76

Crossrefs

Cf. A068145.

Programs

Mathematica

Select[ Union[ Flatten[ Table[a^a - b^b, {a, 1, 40}, {b, 1, a - 1} ]]], PrimeQ ]

PARI

v=[]; for(a=2, 400, forstep(b=a-1, 1, -2, if(ispseudoprime(t=a^a-b^b), v=concat(v,t)))); v \\ Charles R Greathouse IV, Feb 14 2011

Formula

The sum of the reciprocals converges to 0.38150016336280165719931278557192073226416041392427864458688292865... - Cino Hilliard, Dec 15 2002

Extensions

Edited and extended by Robert G. Wilson v and Sascha Kurz, Mar 01 2002