boring numbers
Marc LeBrun
mlb at well.com
Fri Jan 19 17:57:04 CET 2001
The period 1 continued fractions [a a a...] involve taking the square roots
of numbers of the form n^2+1.
The square part of n^2+1 seems always to be a prime congruent to 1 mod
4. This looks to be A002144, although for n<10000 only the 29 values
5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149,
181, 193, 197, 257, 281, 313, 373, 389, 401, 569, 577, 677, and 5741
appear. If I knew enough modern quadratic residue theory, would I be sure
that all such primes would eventually appear? Would I know when each one
would first appear? Would I also be able to characterize the sequence of
square free parts of n^2+1?
Thanks!
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