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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A257770 Table read by rows: numbers k, 0<=k<=9, such that n is a Belgian-k number.

Original entry on oeis.org

0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 3, 5, 6, 8, 9, 0, 1, 4, 5, 8, 9, 3, 4, 8, 9, 2, 3, 8, 9, 1, 2, 8, 9, 0, 1, 8, 9, 0, 8, 9, 8, 9, 0, 2, 4, 6, 8, 0, 1, 3, 4, 6, 7, 9, 0
Offset: 0

Views

Author

Reinhard Zumkeller, May 08 2015

Keywords

Comments

See A106039 for definition of Belgian-k numbers;
T(n,0) = A257778(n); T(n,A257773(n)) = A257779(n);
m is a Belgian-0 number iff T(m,0) = 0.

Examples

			The first 100 rows:
.   0 | 0                     25 | 2,4,9       50 | 0,5     75 | 3,8
.   1 | 0,1                   26 | 0,2,8       51 | 3,4,9   76 | 4
.   2 | 0,2                   27 | 0,7,9       52 | 3,5     77 | 0,7
.   3 | 0,3                   28 | 6,8         53 | 0,5,8   78 | 3
.   4 | 0,4                   29 | 5,7         54 | 0,4,9   79 | 8
.   5 | 0,5                   30 | 0,3,6,9     55 | 0,5     80 | 0,8
.   6 | 0,6                   31 | 0,3,4,7,8   56 | 1,7     81 | 0,1,9
.   7 | 0,7                   32 | 2,4,7,9     57 | 4,9     82 | 2,4
.   8 | 0,8                   33 | 0,3,6,9     58 | 1,6     83 | 6,9
.   9 | 0,9                   34 | 3,6         59 | 3       84 | 0,4
.  10 | 0,1,2,3,4,5,6,7,8,9   35 | 0,3,8       60 | 0,6     85 | 7
.  11 | 0,1,2,3,4,5,6,7,8,9   36 | 0,6,9       61 | 5,6     86 | 2,8
.  12 | 0,2,3,5,6,8,9         37 | 4,7         62 | 0,6,8   87 | 4
.  13 | 0,1,4,5,8,9           38 | 2,5         63 | 0,3,9   88 | 0,8
.  14 | 3,4,8,9               39 | 0,3         64 | 4,8     89 | 4
.  15 | 2,3,8,9               40 | 0,4,8       65 | 4       90 | 0,9
.  16 | 1,2,8,9               41 | 1,2,6,7     66 | 0,6     91 | 1,2
.  17 | 0,1,8,9               42 | 0,2,6,8     67 | 2,9     92 | 4,6
.  18 | 0,8,9                 43 | 1,4,8       68 | 6       93 | 0,9
.  19 | 8,9                   44 | 0,4,8       69 | 3,9     94 | 3,7
.  20 | 0,2,4,6,8             45 | 0,5,9       70 | 0,7     95 | 2
.  21 | 0,1,3,4,6,7,9         46 | 2,6         71 | 0,7,8   96 | 6
.  22 | 0,2,4,6,8             47 | 3           72 | 0,2,9   97 | 1,8
.  23 | 1,3,6,8               48 | 0,8         73 | 3,6     98 | 4
.  24 | 0,4,6                 49 | 6           74 | 1,8     99 | 0,9  .

Links

Crossrefs

Cf. A257773 (row lengths), A257778 (min per row), A257778 (max per row),
Belgian-k numbers, k=0..9: A106039, A106439, A106518, A106596, A106631, A106792, A107014, A107018, A107032, A107043.

Programs

  • Haskell
    a257770 n k = a257770_tabf !! n !! k
a257770_row n = filter belge [0..9] where
   belge k = n == (head $ dropWhile (< n) $
                  scanl (+) k $ cycle $ (map (read . return) . show) n)
a257770_tabf = map a257770_row [0..]

A257778 Smallest k, such that n is a Belgian-k number.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 1, 0, 0, 8, 0, 0, 0, 1, 0, 2, 0, 0, 6, 5, 0, 0, 2, 0, 3, 0, 0, 4, 2, 0, 0, 1, 0, 1, 0, 0, 2, 3, 0, 6, 0, 3, 3, 0, 0, 0, 1, 4, 1, 3, 0, 5, 0, 0, 4, 4, 0, 2, 6, 3, 0, 0, 0, 3, 1, 3, 4, 0, 3, 8, 0, 0, 2, 6, 0, 7
Offset: 0

Views

Author

Reinhard Zumkeller, May 08 2015

Keywords

Comments

See A106039 for definition of Belgian-k numbers;
a(n) = A257770(n,0);
a(n) <= A257779(n); a(A257785(n)) = A257779(A257785(n));
conjecture: a(n) < 9;
a(A106039(n)) = 0; a(A257782(n)) > 0.

Links

Crossrefs

Cf. A106039, A257770, A257773, A257779, A257782.

Programs

  • Haskell
    a257778 = head . a257770_row

A257785 Numbers that are Belgian-k for exactly one k.

Original entry on oeis.org

0, 47, 49, 59, 65, 68, 76, 78, 79, 85, 87, 89, 95, 96, 98, 167, 177, 187, 193, 194, 239, 267, 268, 269, 286, 287, 293, 298, 299, 338, 349, 359, 367, 379, 394, 397, 398, 418, 437, 438, 458, 478, 479, 492, 497, 498, 499, 507, 528, 529, 536, 547, 548, 560, 568
Offset: 1

Views

Author

Reinhard Zumkeller, May 08 2015

Keywords

Comments

See A106039 for definition of Belgian-k numbers;
A257773(a(n)) = 1;
A257778(a(n)) = A257779(a(n)).

Examples

			Let B(n) = A257778(a(n)), the singleton of a(n)-th row in A257770:
.   n |  a(n) | B(n)        n |  a(n) | B(n)         n |  a(n) | B(n)
.  ---+-------+-----     -----+-------+-----     ------+-------+-----
.   1 |     0 |   0       100 |   763 |   4       1000 |  6702 |   6
.   2 |    47 |   3       101 |   766 |   6       1001 |  6706 |   5
.   3 |    49 |   6       102 |   768 |   5       1002 |  6709 |   8
.   4 |    59 |   3       103 |   769 |   8       1003 |  6719 |   3
.   5 |    65 |   4       104 |   779 |   6       1004 |  6725 |   5
.   6 |    68 |   6       105 |   781 |   6       1005 |  6728 |   6
.   7 |    76 |   4       106 |   785 |   5       1006 |  6730 |   4
.   8 |    78 |   3       107 |   787 |   2       1007 |  6736 |   4
.   9 |    79 |   8       108 |   788 |   6       1008 |  6742 |   3
.  10 |    85 |   7       109 |   789 |   6       1009 |  6747 |   3
.  11 |    87 |   4       110 |   790 |   6       1010 |  6748 |   6
.  12 |    89 |   4       111 |   793 |   7       1011 |  6752 |   6
.  13 |    95 |   2       112 |   794 |   7       1012 |  6753 |   6
.  14 |    96 |   6       113 |   795 |   2       1013 |  6755 |   3
.  15 |    98 |   4       114 |   796 |   4       1014 |  6756 |   6
.  16 |   167 |   6       115 |   797 |   8       1015 |  6758 |   6
.  17 |   177 |   4       116 |   798 |   6       1016 |  6766 |   3
.  18 |   187 |   2       117 |   799 |   8       1017 |  6768 |   5
.  19 |   193 |   1       118 |   805 |   4       1018 |  6770 |   4
.  20 |   194 |   2       119 |   807 |   4       1019 |  6772 |   5  .

Links

Crossrefs

Cf. A257770, A257773, A007088, A257778, A257779.

Programs

  • Haskell
    a257785 n = a257785_list !! (n-1)
a257785_list = filter ((== 1) . a257773) [0..]
Showing 1-3 of 3 results.

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