OFFSET
1,1
COMMENTS
This is a famous hard problem and the terms shown are only conjectured values.
The terms shown are not the difference of two powers below 10^19. - Don Reble
One can immediately represent the odd numbers and the multiples of four as differences of two squares. - Don Reble
The terms shown are not the difference of two powers below 10^27. - Mauro Fiorentini, Jan 08 2020
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, Sections D9 and B19.
LINKS
Mauro Fiorentini, Table of n, a(n) for n = 1..119
Alf van der Poorten, Remarks on the sequence of 'perfect' powers.
EXAMPLE
Examples showing that certain numbers are not in the sequence: 10 = 13^3-3^7, 22 = 7^2 - 3^3, 29 = 15^2 - 14^2, 31 = 2^5 - 1, 52 = 14^2 - 12^2, 54 = 3^4 - 3^3, 60 = 2^6 - 2^2, 68 = 10^2 - 2^5, 72 = 3^4 - 3^2, 76 = 5^3 - 7^2, 84 = 10^2 - 2^4, ...
50 = 7^2 - -1^3, 82 = 9^2 - -1^3, 226 = 15^2 - -1^3, 246 = 11^2 - -5^3, 290 = 17^2 - -1^3, ... [Typos corrected by Gerry Myerson, May 14 2008]
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
Don Reble, Oct 12 2002
STATUS
approved