A075824 - OEIS

%I #22 Feb 26 2022 16:12:43

%S 9,11,17,19,21,25,27,33,35,39,41,43,45,49,51,53,57,59,65,67,69,71,73,

%T 75,77,79,81,83,85,87,89,91,93,95,97,99,103,105,107,109,111,113,115,

%U 117,121,123,129,131,133,135,137,139,141,143,145,147,149,151,153,155,157

%N Odd numbers that cannot be expressed as 2^k - 3^m where k and m are integers.

%C All listed terms can be certified by considering 2^k - 3^m modulo 2552550. [_Max Alekseyev_, Feb 08 2010]

%D R. K. Guy, Unsolved Problems in Number Theory, D9.

%D T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge University Press, 1986.

%H T. Metsankyla, <a href="https://doi.org/10.1090/S0273-0979-03-00993-5">Catalan's Conjecture : Another old Diophantine problem solved</a>, Bull. Amer. Math. Soc. 41 (2004), 43-57.

%H Wikipedia, <a href="http://www.wikipedia.org/wiki/Catalan%27s_conjecture">Catalan's conjecture</a>

%e 5 doesn't belong to the sequence because it can be expressed as 2^3 - 3^1.

%Y Cf. A074981, A192110, A328077.

%K nonn

%O 1,1

%A _Felice Russo_, Oct 14 2002

%E Inserted "odd" in definition. - _N. J. A. Sloane_, Jan 30 2009

%E _Jon E. Schoenfield_ observed that 49 was missing, Jan 30 2009

%E More terms from _Max Alekseyev_, Feb 08 2010