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

1,1

Comments

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

References

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

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

Links

Table of n, a(n) for n=1..61.

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

Wikipedia, Catalan's conjecture

Example

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

Crossrefs

Cf. A074981, A192110, A328077.

Sequence in context: A216976 A236390 A048464 * A228951 A108113 A111391

Adjacent sequences: A075821 A075822 A075823 * A075825 A075826 A075827

Keyword

nonn

Author

Felice Russo, Oct 14 2002

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

Status

approved