A162408 Solutions x to the equation x^x-y^y = some prime number for any y.

2, 3, 4, 5, 7, 8, 11, 13, 15, 17, 19, 23, 26, 30, 42, 47, 53, 65, 73, 77, 84, 92, 100, 101, 106, 110, 116, 120, 122, 122, 124, 133, 137, 163, 167, 173, 173

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 02 2009

Keywords

• nonn

Comments

These are the numbers a in the definition of A068146.

If there are two solutions, like with (x,y) = (17,12) and (x,y) = (17,16) with

the same x, only one instance of x is placed into the sequence, so there is no

1-to-1 correspondence with terms in A068146.

The corresponding set of y contains at least the numbers 1 to 6, 10, 12, 14, 16, 17, 19, 20, 22 etc

Examples

			Triples (x,y,prime) are (2,1,3), (3,2,23), (4,3,229), (5,2,3121), (7,6,776887),
(8,5,16774091), (11,10,275311670611), (13,6,302875106545597), (15,4,437893890380859119),
(17,12,827240252970236315921), (17,16,808793517812627212561) etc
		

Crossrefs

Cf. A068146

Programs

Mathematica

f[a_,b_]:=a^a-b^b; lst={};Do[Do[If[a>b,p=f[a,b]];If[PrimeQ[p],AppendTo[lst, a]],{b,4*4!}],{a,5*4!}];Union[lst]

Extensions

Edited and extended by R. J. Mathar, Sep 16 2009