More conjectures!
David Wilson
davidwwilson at comcast.net
Mon Jan 8 06:14:06 CET 2007
> %F A102380 Conjecture: the sequence can be generated by taking the powers
> of three and the numbers 2, 4, 6, 7, 14, and applying the rule 'if x is in
> sequence then so is 5x'. - Ralf Stephan, Jan 07 2004
> %N A102380 Moduli n for which the Fibonacci numbers (mod n) form a
> complete residue class.
This description of A102380 given above does not agree with A102380 in the
database. I would guess that A102830 was added to the database, Ralph
copied it, then A102380 was removed from the database as a duplicate of
A079002 and replaced with a new sequence.
At any rate, supposing A102380 was a duplicate of A079002, the conjecture is
not correct. A true characterization of A079002 is given on the current %F
line. This characterization:
%F A079002 Consists of the integers of the form: 5^k, 2*5^k, 4*5^k, 3^j*5^k,
6*5^k, 7*5^k and 14*5^k. [see Concrete Mathematics]
is correct if slightly redundant, since numbers of the form 3^j*5^k include
numbers of the form 5^k.
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