A162573 Primes of the form 2^x+x*y+2^y, with x and y integers of any sign.

2, 3, 5, 13, 17, 89, 137, 157, 257, 523, 547, 2089, 2659, 4217, 8821, 16553, 34981, 65537, 65761, 262433, 524309, 524353, 524971, 2097223, 2097289, 2097427, 2099431, 8390909, 10486243, 35652109, 134217757, 536871089, 536873279

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 06 2009

Keywords

• nonn

Comments

Allowing either sign in x or y leads to fractions 2^x or 2^y if x or y are negative,

but since the sum must be integer, only the case x=y=-1 matters in these quadrants. - R. J. Mathar, Jul 31 2007

Programs

Mathematica

f[x_,y_]:=2^x+x*y+2^y; lst={};Do[Do[p=f[x,y];If[PrimeQ[p],AppendTo[lst, p]],{y,-5!,6!}],{x,-5!,6!}];Take[Union[lst],5! ]