Gaussian Smoothness
Ed Pegg Jr
edp at wolfram.com
Tue Jan 11 16:53:04 CET 2005
I rather like the sequence of adjacent smooth numbers.
http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A002072
I've been trying to extend that concept of smoothness.
I'll say that 7950+9650i is G6-smooth, since all of its prime Gaussian
factors have real and imaginary parts ≤6.
Here are two large adjacent G5-smooth numbers. These popped out after
a 4-week search. I keep finding more, so I doubt very much that I've
found the actual "OEIS sequence"-worthy numbers. The search is starting
to get more interesting, though.
28593+6426i = (1+2i)^5×(3)^3×(3+2i)×(5+2i)
28594+6426i = (1+i)^3×(1+4i)×(2+3i)×(4+i)^2×(5+4i)^2
--Ed Pegg Jr
More information about the SeqFan
mailing list