[seqfan] Re: Another surprising omission from OEIS

[Michael Porter]

I get the same numbers.  Here is the PARI program I used:
digits(n,b) = if(n<b, [n], concat(digits(floor(n/b),b),n%b))\Q
is_repdigit(d) = {local(a,r);r=1;a=d[1];for(i=2,matsize(d)[2],if(a!=d[i],r=0));r}\Q
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++))

The first line generates a vector of digits (e.g. digits(1234,10) = [1, 2, 3, 4]).  The second line determines if the digits in that vector are all the same.  The three-digit restriction is handled by the "n>=b^2+b+1" in the while loop.

I added the "\Q" to the end of the first two lines so it can be used in a sequence.

- Michael



--- On Tue, 11/10/09, Andrew Weimholt <andrew.weimholt at gmail.com> wrote:

From: Andrew Weimholt <andrew.weimholt at gmail.com>
Subject: [seqfan]  Another surprising omission from OEIS
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Date: Tuesday, November 10, 2009, 5:58 PM

Numbers that are repdigits with length > 2 in some base.
(length > 2 because all numbers n > 2, are trivially represented as 11
in base n-1)

       7 = 111     base 2
      13 = 111     base 3
      15 = 1111    base 2
      21 = 111     base 4
      26 = 222     base 3
      31 = 11111   base 2 (also 111 base 5)
      40 = 1111    base 3
      42 = 222     base 4
      43 = 111     base 6
      57 = 111     base 7
      62 = 222     base 5
      63 = 111111  base 2 (also 333 base 4)
      73 = 111     base 8
      80 = 2222    base 3
      85 = 1111    base 4
      86 = 222     base 6
      91 = 111     base 9
      93 = 333     base 5
     111 = 111     base 10
     114 = 222     base 7
     121 = 11111   base 3
     124 = 444     base 5
     127 = 1111111 base 2
     129 = 333     base 6
     133 = 111     base 11

7, 13, 15, 21, 26, 31, 40, 42, 43, 57, 62, 63, 73, 80, 85, 86,
91, 93, 111, 114, 121, 124, 127, 129, 133, 146, 156, 157,
170, 171, 172, 182, 183, 211, 215, 219, 222, 228, 241, 242,
255, 259, 266, 273, 285, 292, 307, 312, 314, 333, 341, 342,
343, 364, 365, 366, 381, 399, 400, 421, 422, 438, 444, 455,
463, 468, 471, 482, 507, 511, 518, 532, 546, 549, 553, 555,
585, 601, 614, 624, 628, 633, 637, 651, 665, 666, 682, 686,
703, 723, 728, 732, 757, 762, 777, 781, 785, 798, 800, 813,
819, 820, 842, 844, 871, 888, 915, 921, 926, 931, 942, 964,
993, 999, 1014, 1023, 1029, 1036, 1055, 1057, 1064, 1092,
1093, 1098, 1099,1106, 1111

Andrew


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