A075824 Odd numbers that cannot be expressed as 2^k - 3^m where k and m are integers.

9, 11, 17, 19, 21, 25, 27, 33, 35, 39, 41, 43, 45, 49, 51, 53, 57, 59, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 103, 105, 107, 109, 111, 113, 115, 117, 121, 123, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157

Offset: 1

Author

Felice Russo, Oct 14 2002

Keywords

• nonn

Comments

All listed terms can be certified by considering 2^k - 3^m modulo 2552550. [Max Alekseyev, Feb 08 2010]

Examples

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

References

• R. K. Guy, Unsolved Problems in Number Theory, D9.
• T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge University Press, 1986.

Links

• T. Metsankyla, Catalan's Conjecture : Another old Diophantine problem solved, Bull. Amer. Math. Soc. 41 (2004), 43-57.
• Wikipedia, Catalan's conjecture

Crossrefs

Cf. A074981, A192110, A328077.

Extensions

Inserted "odd" in definition. - N. J. A. Sloane, Jan 30 2009

Jon E. Schoenfield observed that 49 was missing, Jan 30 2009

More terms from Max Alekseyev, Feb 08 2010