

A075824


Odd numbers that cannot be expressed as 2^n3^m where n and m are integers.


2



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
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OFFSET

1,1


COMMENTS

All listed terms can be certified by considering 2^n3^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), 4357.
Wikipedia, Catalan's conjecture


EXAMPLE

5 doesn't belong to the sequence because it can be expressed as 2^33^1.


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



