3,1

a(6) and a(7) are only conjectures; the earlier terms have (apparently) been proved.

A. Bremner and P. Morton, A new characterization of the integer 5906, Manuscripta Math. 44 (1983) 187-229; MR 84i:10016.

Steve Finch, On a Generalized Fermat-Wiles Equation

Dave Rusin, Seeking counterexamples to FLT in other rings

a(3) = 6 = (17/21)^3 + (37/21)^3

a(4) = 5906 = (25/17)^4 + (149/17)^4

a(5) = 68101 = (15/2)^5 + (17/2)^5

a(6) <= 164634913 = (44/5)^6 + (117/5)^6 (John W. Layman, Oct 20, 2005)

a(7) <= 69071941639 = (63/2)^7 + (65/2)^7

Adjacent sequences: A111149 A111150 A111151 this_sequence A111153 A111154 A111155

Sequence in context: A115431 A116135 A011788 this_sequence A003191 A000438 A061109

nonn

David W. Wilson (davidwwilson(AT)comcast.net), Oct 19 2005