[seqfan] Re: Another surprising omission from OEIS
Alonso Del Arte
alonso.delarte at gmail.com
Thu Nov 12 17:08:02 CET 2009
The title of this thread has bothered me since I read the first post in it.
I think the reason is that I don't find the omission of a keyword:base
sequence surprising at all. Most math amateurs, if they stick to it,
eventually lose interest in base sequences. Most professional mathematicians
probably feel that they must specialize in the topic of radix representation
if they're going to give it any significant portion of their time. Modular
arithmetic, on the other hand, is so fundamental to number theory that the
absence of the orderly numbers from the OEIS for so long I do find genuinely
surprising. Well, that's just my opinion, for what it's worth.
Al
On Thu, Nov 12, 2009 at 3:29 AM, Michael Porter <ic_designer at verizon.net>wrote:
>
> No problem.
>
> - Michael
>
> --- On Thu, 11/12/09, Andrew Weimholt <andrew.weimholt at gmail.com> wrote:
>
> From: Andrew Weimholt <andrew.weimholt at gmail.com>
> Subject: [seqfan] Re: Another surprising omission from OEIS
> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Date: Thursday, November 12, 2009, 12:22 AM
>
> On Wed, Nov 11, 2009 at 11:21 PM, Michael Porter
> <ic_designer at verizon.net> wrote:
> >
> > This case is different from most sequences in that adding zero to the
> start of the sequence requires that you allow 000 to fit the definition of a
> repdigit, which is really contrived. And it's unlikely that someone
> searching for repdigits would include 000 in his search.
> >
> > - Michael
> >
>
> I agree that it is contrived, but I submitted the sequence with 0
> included. After sleeping on it and reading some of the comments from
> the other seqfans, I was won over by the "error on the side of
> inclusion" principle.
>
> See submission lines below. I also submitted the sequence of numbers
> which are repdigits of length > 2 in more than 1 base.
>
> Andrew
>
> %I A167782
> %S A167782
> 0,7,13,15,21,26,31,40,42,43,57,62,63,73,80,85,86,91,93,111,114,121,124,
> %T A167782
> 127,129,133,146,156,157,170,171,172,182,183,211,215,219,222,228,241,
> %U A167782
> 242,255,259,266,273,285,292,307,312,314,333,341,342,343,364,365,366
> %N A167782 Numbers that are repdigits with length > 2 in some base.
> %C A167782 Definition requires "length > 2" because all numbers, n
> > 2, are trivially represented as "11" in base n-1.
> %C A167782 0 included at the suggestion of Franklin T. Adams-Watters
> (and others) as 0 = 000 in any base.
> %C A167782
> %e A167782 26 is in the list because 26 (base 10) = 222 (base 3)
> %o A167782 (PARI) digits(n,b) = if(n<b, [n],
> concat(digits(floor(n/b),b),n%b))
> %o A167782 is_repdigit(d) =
> {local(a,r);r=1;a=d[1];for(i=2,matsize(d)[2],if(a!=d[i],r=0));r}
> %o A167782
> for(n=1,1200,b=2;while(n>=b^2+b+1,d=digits(n,b);if(is_repdigit(d),print(n,"
> = ",d," base ",b));b++))
> %o A167782 --Michael Porter
> %Y A167782 Cf. A010785 - Repdigits (base 10)
> %Y A167782 Cf. A167783 - Numbers that are repdigits with length > 2
> in more than one base.
> %Y A167782 Cf. A053696 - Numbers which are repunits in some base
> %Y A167782 Cf. A158235 - Numbers n whose square can be represented as
> a repdigit number in some base < n
> %K A167782 nonn
> %O A167782 1,2
> %A A167782 Andrew Weimholt (andrew(AT)weimholt.com), Nov 12 2009
>
> %I A167783
> %S A167783
> 0,31,63,255,273,364,511,546,728,777,931,1023,1365,1464,2730,3280,3549,
> %T A167783
> 3783,3906,4095,4557,6560,7566,7812,8191,9114,9331,9841,10507,11349,
> %U A167783
> 11718,13671,14043,14763,15132,15624,16383,18291,18662,18915,19608
> %N A167783 Numbers that are repdigits with length > 2 in more than one
> base.
> %C A167783 Definition requires "length > 2" because all numbers, n
> > 2, are trivially represented as "11" in base n-1.
> %C A167783 0 included at the suggestion of Franklin T. Adams-Watters
> (and others) as 0 = 000 in any base.
> %C A167783
> %e A167783 31 is in the list because 31 (base 10) = 11111 (base 2) =
> 111 (base 5)
> %Y A167783 Cf. A167782 - Numbers that are repdigits with length > 2
> in some base
> %Y A167783 Cf. A010785 - Repdigits (base 10)
> %Y A167783 Cf. A053696 - Numbers which are repunits in some base
> %Y A167783 Cf. A158235 - Numbers n whose square can be represented as
> a repdigit number in some base < n
> %K A167783 nonn
> %O A167783 1,2
> %A A167783 Andrew Weimholt (andrew(AT)weimholt.com), Nov 12 2009
>
>
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