login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A162408 Solutions x to the equation x^x-y^y = some prime number for any y. 0
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 (list; graph; refs; listen; history; text; internal format)
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 A176176

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 4 02:16 EST 2022. Contains 358544 sequences. (Running on oeis4.)