I wonder if there's a connection with the fact that n=23 is the least n for which the cyclotomic ring Z[exp(2pi*i/n)] has non-unique factorization. (And all primes p >= 23 have the property that Z[exp(2pi*i/p)] is a non-UFD.) More monstrous moonshine? --Dan ----------- Rich wrote: << This looks like an interesting puzzle. His sum of k = z^-3 + ... + z^3 can also be read as the sum of a few cosines, or as the sum of a geometric series. It should be easy to gather more data. ----- Forwarded message from boston@MATH.WISC.EDU ----- Date: Wed, 29 Apr 2009 13:32:25 -0400 From: Nigel Boston <boston@MATH.WISC.EDU> When computing the Koetter-Vontobel lower bound for minimum pseudoweight of the binary Golay code, a certain term came out as 15.9996. My engineering collaborator rounded this to 16 but the fact that it's so close to an integer but not actually an integer is in itself interesting. The term is actually 4+2k, where k = z^-3 + z^-2 + z^-1 + 1 + z + z^2 + z^3 and z is the 23rd root of unity exp(2\pi i/23). k is 5.99977967. . . .

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_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele