A075824 - OEIS

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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

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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