[seqfan] Re: Another surprising omission from OEIS
Michael Porter
ic_designer at verizon.net
Thu Nov 12 09:29:18 CET 2009
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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