A theoretical question -- sieving via n mod x

[franktaw at netscape.net]

Assuming that evaluating your function is fast, this should be very 
efficient.  Combining results in different moduli is essentially just 
Euclid's algorithm (for the GCD) -- which is quite fast -- followed by 
a couple of multiplications and an addition.

Franklin T. Adams-Watters

-----Original Message-----
From: Andrew Plewe <aplewe at sbcglobal.net>

I'm curious how a sieve, similar to the sieve of Erosthanese, would
"perform".  The basic idea is this: suppose that n is some number that 
you
want to factor. Assume that you can map, for x = 0 to some upper bound 
less
than the smallest factor of n, n == a mod x --> f == b mod x, where f 
is a
factor of n. Say, for instance:

n == 2 mod 3, therefore f == 1 mod 3
n == 1 mod 4, therefore f == 3 mod 4
n == 4 mod 5, therefore f == 2 mod 5

& etc.

Thus we could establish a "profile" for f, which can be turned into a 
sieve
by finding all integers congruent to 1 mod 3, then a subset congruent 
to 3
mod 4, then a subset of that congruent to 2 mod 5, etc. My question is 
how
"quickly" can we narrow in on possible values for f by using this 
sieve? I
think something like this may be possible for values of n with certain
properties, but I'm not sure how well it'd perform.

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There are three seqs titled "Number of weighted voting procedures"
http://www.research.att.com/~njas/sequences/A005254
http://www.research.att.com/~njas/sequences/A005256
http://www.research.att.com/~njas/sequences/A005257

Could somebody define the term "weighted voting procedure"
and add the information to differentiate the seqs?




Hello seqfans,

Here I see two entries with the same name:

A030225 Number of n-celled polyhexes (hexagonal polyominoes) with bilateral symmetry.
A002215 Number of polyhexes with n hexagons, having reflectional symmetry. 


Probably, the second one should be about "restricted" polyhexes, BUT, there are two entries about restricted polyhexes:

A002216 Harary-Read numbers: restricted hexagonal polyominoes (cata-polyhexes) with n cells. 
A002212 Number of restricted hexagonal polyominoes with n cells. 


On top of that, if a2216 is the number of cata-polyhexes, then what is
A038142 Number of planar cata-polyhexes with n cells.

I am completely confused.

Best, Tanya


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You did such a great job removing duplicate sequences. How about duplicate definitions:

A002212 Number of restricted hexagonal polyominoes with n cells.
A005963 Number of restricted hexagonal polyominoes with n cells. 

Tanya


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A001168 Number of fixed polyominoes with n cells.
A006762 Number of fixed polyominoes with n cells. 


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Let me remind folks that the primary purpose
of the OEIS is to give pointers to the literature,
you can find out who else has studied the same sequence.

I don't claim to give precise definitions for every single

If you find two sequences with the same definition
("Related to the enumeration of ***", say),
feel free to track down the references and

Neil