terms lack

[kohmoto]

    To Dean Hicherson

    Thanks for editing my sequences.
    And thanks for a good explanation about "completeness".
    Now, I understand that  the  purpose of OEIS is "Identification of 
sequences", it is necessary.

    Should A038362 be deleted?
    Still, I think that it should exist , because a sequence is a mapping 
from N to N, so a subset of the images is also a good information for 
understanding the mapping.

    Yasutoshi


----- Original Message ----- 
From: "Dean Hickerson" <dean at math.ucdavis.edu>
To: <seqfan at ext.jussieu.fr>
Sent: Monday, November 06, 2006 6:39 PM
Subject: Re: terms lack


> Mostly to Yasutoshi Kohmoto <zbi74583 at boat.zero.ad.jp>:
>
>> Recently I updated more terms of A054572, which are calculated by
>> Richard Mathar.
>> And Neil claimed or got angry.
>> He said, "You are red card. Don't submit a wrong sequences"
>> I am exaggerating a little.
>> These words are not exactly what he wrote.
>>
>> To Neil
>> They are correct, not "wrong".
>> It is only not complete.
>
> The terms that are listed in a sequence should be the start of the 
> sequence.
> If there are missing terms in between the listed ones, then the sequence
> entry is not just incomplete, it's wrong.
>
> If you've computed some terms of a sequence, but you're not sure if there
> are smaller ones that you've missed, then you should only include the ones
> that you're sure are at the start of the sequence.  You can add a comment
> about the larger terms, stating that it's not known if there are smaller 
> ones.
> For example, the "EXTENSIONS" lines for the sequence A000043 (Mersenne
> exponents) mention some recently discovered terms.  But there might be
> some smaller ones, so these are not included in the sequence.
>
>> I defined many "divisor" functions and calculated many Amicable Numbers 
>> and
>> Perfect Numbers using those functions.
>> And I submitted them as sequences to  OEIS.
>>
>> http://www.research.att.com/~njas/sequences/?q=kohmoto+amicable&sort=0&fmt=0&language=english&go=Search
>>
>> http://www.research.att.com/~njas/sequences/?q=kohmoto+perfect&sort=0&fmt=0&language=english&go=Search
>>
>> I suppose that they are almost complete but some of them might not be
>> complete.
>
> I've found missing terms for several of your sequences:
>
>
> Sequences A045613 and A045614 ("Super Unitary Amicable Number") consist
> of pairs of distinct numbers a and b such that
>
>    usigma(usigma(a)) = usigma(usigma(b)) = a+b.
>
> (The definitions don't make this clear, but A045613 contains the smaller
> members of the pairs and A045614 contains the larger members.  Also 
> they're
> sorted by their smallest members, so 155 comes before 142 in A045614.) 
> The
> first 3 pairs that you've listed are (105, 155), (110, 142) and (2145, 
> 3055).
> But you've missed several smaller ones:
>
>    (33, 35), (208, 224), (268, 272), (455, 601), (695, 1033), (812, 956),
>    (1609, 1847), (1808, 2512), (1892, 3004), (1913, 2407), (2096, 2224)
>
>
> A051594 and A051595 are "(-1)sigma amicable numbers".  (Again, the 
> definition
> doesn't make it clear that A051595 has the smaller terms and A051594 has 
> the
> larger terms.)  The first pair that you've listed is (1969706592, 
> 2236072608).
> But there are many smaller ones, starting with:
>
>    (429552, 466200), (497808, 604656), (800496, 1103760).
>
>
> A036471-A036474 are defined as "Amicable quadruple: 4 different numbers
> which satisfy sigma(a)=sigma(b)=sigma(c)=sigma(d)=a+b+c+d".  The first
> quadruple that you've listed has smallest element
> 342151462276356306033089201934180, but here's a much smaller one:
>
>    (3270960, 3361680, 3461040, 3834000)
>
> (I think that's the smallest one, but I could be wrong.)  If someone can
> determine the first several terms of this sequence, then it should be
> edited; otherwise it should be deleted.
>
>
> In some of your sequences, I wasn't able to find any smaller terms, but 
> the
> ones that you've listed are so large that I'm not at all confident that 
> they
> are the smallest ones.  For example, A038362 and A038363 are defined as
> "A Rational Amicable Number: two different numbers a, b which satisfies 
> the
> following equation: sigma(a)=sigma(b)=(a+b)^3/(a^2+b^2)", and the smallest
> pair that you've included is:
>
>    (26403469440047700, 30193441130006700)
>
> Do you have any reason to think that that's the smallest such pair?  If 
> not,
> and if you can't determine what the first few terms really are, then the
> sequence should be deleted.
>
>
> I've only looked at a few of your sequences, but that's enough to convince
> me that they should all be checked.
>
> Neil, I'll submit corrections for A045613, A045614, A051594, and A051595,
> but I'm not going to work on the others.  Maybe they should be deleted or
> marked as "probation" until the author or someone else fixes them.
>
> Dean Hickerson
> dean at math.ucdavis.edu
>