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

1,1

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

Links

Table of n, a(n) for n=1..37.

Example

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

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]

Crossrefs

Cf. A068146

Sequence in context: A269870 A307824 A081730 * A348284 A162721 A378441

Adjacent sequences: A162405 A162406 A162407 * A162409 A162410 A162411

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jul 02 2009

Extensions

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

Status

approved