A106039 -id:A106039 - cp's OEIS frontend

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

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

Reinhard Zumkeller, May 08 2015

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.

			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  .

Reinhard Zumkeller, Rows n = 0..1000 of triangle, flattened

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.

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..]

A106596 Belgian-3 numbers.

Original entry on oeis.org

3, 10, 11, 12, 14, 15, 21, 23, 30, 31, 33, 34, 35, 39, 47, 51, 52, 59, 63, 69, 73, 75, 78, 94, 100, 101, 102, 103, 104, 105, 107, 110, 111, 112, 113, 115, 116, 120, 123, 133, 141, 146, 147, 151, 153, 154, 158, 159, 163, 164, 166, 168, 183, 185, 191, 196

Offset: 1

Eric Angelini, Jun 07 2005

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

See A106039 for definition and link.
Belgian-k numbers, k=0..9: A106039, A106439, A106518, A106596, A106631, A106792, A107014, A107018, A107032, A107043.
Cf. A257770.

a106596 n = a106596_list !! (n-1)
a106596_list = filter belge3 [3..] where
   belge3 x = x == (head $ dropWhile (< x) $
                    scanl (+) 3 $ cycle (map (read . return) $ show x))
-- Reinhard Zumkeller, May 08 2015

belgianQ[n_, k_] := If[n < k, False, Block[{id = Join[{0}, IntegerDigits@ n]}, MemberQ[ Accumulate@ id, Mod[n - k, Plus @@ id]] ]]; Select[ Range@ 200, belgianQ[#, 3] &] (* Robert G. Wilson v, May 06 2011 *)

Offset changed by Reinhard Zumkeller, May 08 2015

A106439 Belgian-1 numbers.

Original entry on oeis.org

1, 10, 11, 13, 16, 17, 21, 23, 41, 43, 56, 58, 74, 81, 91, 97, 100, 101, 106, 110, 111, 113, 115, 121, 122, 130, 131, 137, 142, 155, 157, 161, 170, 171, 172, 178, 179, 181, 184, 188, 193, 201

Offset: 1

Eric Angelini, Jun 07 2005

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

See A106039 for definition and link.
Belgian-k numbers, k=0..9: A106039, A106439, A106518, A106596, A106631, A106792, A107014, A107018, A107032, A107043.
Cf. A257770.

a106439 n = a106439_list !! (n-1)
a106439_list = filter belge1 [1..] where
   belge1 x = x == (head $ dropWhile (< x) $
                    scanl (+) 1 $ cycle (map (read . return) $ show x))
-- Reinhard Zumkeller, May 08 2015

belgianQ[n_, k_] := If[n < k, False, Block[{id = Join[{0}, IntegerDigits@ n]}, MemberQ[ Accumulate@ id, Mod[n - k, Plus @@ id]] ]]; Select[ Range@ 202, belgianQ[#, 1] &] (* Robert G. Wilson v, May 06 2011 *)

A106518 Belgian-2 numbers.

Original entry on oeis.org

2, 10, 11, 12, 15, 16, 20, 22, 25, 26, 32, 38, 41, 42, 46, 67, 72, 82, 86, 91, 95, 100, 101, 102, 103, 105, 107, 110, 111, 112, 113, 115, 116, 120, 121, 122, 123, 124, 125, 130, 131, 132, 134, 136, 138, 141, 142, 143

Offset: 1

Eric Angelini, Jun 07 2005

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

See A106039 for definition and link.
Belgian-k numbers, k=0..9: A106039, A106439, A106518, A106596, A106631, A106792, A107014, A107018, A107032, A107043.
Cf. A257770.

a106518 n = a106518_list !! (n-1)
a106518_list = filter belge2 [2..] where
   belge2 x = x == (head $ dropWhile (< x) $
                    scanl (+) 2 $ cycle (map (read . return) $ show x))
-- Reinhard Zumkeller, May 08 2015

belgianQ[n_, k_] := If[n < k, False, Block[{id = Join[{0}, IntegerDigits@ n]}, MemberQ[ Accumulate@ id, Mod[n - k, Plus @@ id]] ]]; Select[ Range@ 145, belgianQ[#, 2] &] (* Robert G. Wilson v, May 06 2011 *)

Offset changed by Reinhard Zumkeller, May 08 2015

A106631 Belgian-4 numbers.

Original entry on oeis.org

4, 10, 11, 13, 14, 20, 21, 22, 24, 25, 31, 32, 37, 40, 43, 44, 51, 54, 57, 64, 65, 76, 82, 84, 87, 89, 92, 98, 100, 101, 104, 110, 111, 112, 114, 116, 121, 122, 124, 125, 127, 128, 137, 140, 141, 142, 144, 145, 148, 149, 151, 154, 158, 172, 177, 191, 196

Offset: 1

Eric Angelini, Jun 07 2005

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

See A106039 for definition and link.
Belgian-k numbers, k=0..9: A106039, A106439, A106518, A106596, A106631, A106792, A107014, A107018, A107032, A107043.
Cf. A257770.

a106631 n = a106631_list !! (n-1)
a106631_list = filter belge4 [4..] where
   belge4 x = x == (head $ dropWhile (< x) $
                    scanl (+) 4 $ cycle (map (read . return) $ show x))
-- Reinhard Zumkeller, May 08 2015

belgianQ[n_, k_] := If[n < k, False, Block[{id = Join[{0}, IntegerDigits@ n]}, MemberQ[ Accumulate@ id, Mod[n - k, Plus @@ id]] ]]; Select[ Range@ 199, belgianQ[#, 4] &] (* Robert G. Wilson v, May 06 2011 *)

Offset changed by Reinhard Zumkeller, May 08 2015

A106792 Belgian-5 numbers.

Original entry on oeis.org

5, 10, 11, 12, 13, 29, 38, 45, 50, 52, 53, 55, 61, 100, 101, 102, 110, 111, 114, 120, 121, 124, 125, 130, 131, 132, 134, 135, 136, 137, 138, 139, 140, 145, 148, 150, 151, 160, 174, 175, 182, 186, 191, 195, 211

Offset: 1

Eric Angelini, Jun 07 2005

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

See A106039 for definition and link.
Belgian-k numbers, k=0..9: A106039, A106439, A106518, A106596, A106631, A106792, A107014, A107018, A107032, A107043.
Cf. A257770.

a106792 n = a106792_list !! (n-1)
a106792_list = filter belge5 [5..] where
   belge5 x = x == (head $ dropWhile (< x) $
                    scanl (+) 5 $ cycle ((map (read . return) . show) x))
-- Reinhard Zumkeller, May 08 2015

belgianQ[n_, k_] := If[n < k, False, Block[{id = Join[{0}, IntegerDigits@ n]}, MemberQ[ Accumulate@ id, Mod[n - k, Plus @@ id]] ]]; Select[ Range@ 211, belgianQ[#, 5] &] (* Robert G. Wilson v, May 06 2011 *)

Offset changed by Reinhard Zumkeller, May 08 2015

A107014 Belgian-6 numbers.

Original entry on oeis.org

6, 10, 11, 12, 20, 21, 22, 23, 24, 28, 30, 33, 34, 36, 41, 42, 46, 49, 58, 60, 61, 62, 66, 68, 73, 83, 92, 96, 100, 101, 102, 103, 110, 111, 112, 113, 114, 118, 120, 121, 122, 123, 126, 127, 128, 129, 130, 131, 132, 133, 134, 136, 138, 143, 150, 155, 156

Offset: 1

Eric Angelini, Jun 07 2005

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

See A106039 for definition and link.
Belgian-k numbers, k=0..9: A106039, A106439, A106518, A106596, A106631, A106792, A107014, A107018, A107032, A107043.
Cf. A257770.

a107014 n = a107014_list !! (n-1)
a107014_list = filter belge6 [6..] where
   belge6 x = x == (head $ dropWhile (< x) $
                    scanl (+) 6 $ cycle (map (read . return) $ show x))
-- Reinhard Zumkeller, May 08 2015

belgianQ[n_, k_] := If[n < k, False, Block[{id = Join[{0}, IntegerDigits@ n]}, MemberQ[ Accumulate@ id, Mod[n - k, Plus @@ id]] ]]; Select[ Range@ 159, belgianQ[#, 6] &] (* Robert G. Wilson v, May 06 2011 *)

Offset changed by Reinhard Zumkeller, May 08 2015

A107018 Belgian-7 numbers.

Original entry on oeis.org

7, 10, 11, 21, 27, 29, 31, 32, 37, 41, 56, 70, 71, 77, 85, 94, 100, 101, 103, 106, 110, 111, 112, 113, 117, 118, 119, 122, 127, 128, 131, 133, 143, 152, 173, 176, 201, 205

Offset: 1

Eric Angelini, Jun 07 2005

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

See A106039 for definition and link.
Belgian-k numbers, k=0..9: A106039, A106439, A106518, A106596, A106631, A106792, A107014, A107018, A107032, A107043.
Cf. A257770.

a107018 n = a107018_list !! (n-1)
a107018_list = filter belge7 [7..] where
   belge7 x = x == (head $ dropWhile (< x) $
                     scanl (+) 7 $ cycle (map (read . return) $ show x))
-- Reinhard Zumkeller, May 08 2015

belgianQ[n_, k_] := If[n < k, False, Block[{id = Join[{0}, IntegerDigits@ n]}, MemberQ[ Accumulate@ id, Mod[n - k, Plus @@ id]] ]]; Select[ Range@ 206, belgianQ[#, 7] &] (* Robert G. Wilson v, May 06 2011 *)

Offset changed by Reinhard Zumkeller, May 08 2015

A107032 Belgian-8 numbers.

Original entry on oeis.org

8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 26, 28, 31, 35, 40, 42, 43, 44, 48, 53, 62, 64, 71, 74, 75, 79, 80, 86, 88, 97, 100, 101, 102, 104, 105, 106, 108, 109, 110, 111, 112, 113, 115, 117, 118, 119, 120, 121, 123, 126, 129, 132, 135, 139, 141, 142, 144

Offset: 1

Eric Angelini, Jun 07 2005

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

See A106039 for definition and link.
Belgian-k numbers, k=0..9: A106039, A106439, A106518, A106596, A106631, A106792, A107014, A107018, A107032, A107043.
Cf. A257770.

a107032 n = a107032_list !! (n-1)
a107032_list = filter belge8 [8..] where
   belge8 x = x == (head $ dropWhile (< x) $
                    scanl (+) 8 $ cycle (map (read . return) $ show x))
-- Reinhard Zumkeller, May 08 2015

belgianQ[n_, k_] := If[n < k, False, Block[{id = Join[{0}, IntegerDigits@ n]}, MemberQ[ Accumulate@ id, Mod[n - k, Plus @@ id]] ]]; Select[ Range@ 148, belgianQ[#, 8] &] (* Robert G. Wilson v, May 06 2011 *)

Offset changed by Reinhard Zumkeller, May 08 2015

A107043 Belgian-9 numbers.

Original entry on oeis.org

9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 25, 27, 30, 32, 33, 36, 45, 51, 54, 57, 63, 67, 69, 72, 81, 83, 90, 93, 99, 100, 101, 102, 104, 105, 108, 109, 110, 111, 115, 117, 119, 120, 121, 122, 123, 124, 126, 129, 130, 135, 139, 140, 141, 142, 144, 146, 149, 153

Offset: 1

Eric Angelini, Jun 07 2005

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

See A106039 for definition and link.
Belgian-k numbers, k=0..9: A106039, A106439, A106518, A106596, A106631, A106792, A107014, A107018, A107032, A107043.
Cf. A257770.

a107043 n = a107043_list !! (n-1)
a107043_list = filter belge9 [9..] where
   belge9 x = x == (head $ dropWhile (< x) $
                    scanl (+) 9 $ cycle (map (read . return) $ show x))
-- Reinhard Zumkeller, May 08 2015

belgianQ[n_, k_] := If[n < k, False, Block[{id = Join[{0}, IntegerDigits@ n]}, MemberQ[ Accumulate@ id, Mod[n - k, Plus @@ id]] ]]; Select[ Range@ 155, belgianQ[#, 9] &] (* Robert G. Wilson v, May 06 2011 *)

Offset changed by Reinhard Zumkeller, May 08 2015

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

A106596 Belgian-3 numbers.

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Mathematica

Extensions

A106439 Belgian-1 numbers.

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Mathematica

A106518 Belgian-2 numbers.

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Mathematica

Extensions

A106631 Belgian-4 numbers.

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Mathematica

Extensions

A106792 Belgian-5 numbers.

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Mathematica

Extensions

A107014 Belgian-6 numbers.

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Mathematica

Extensions

A107018 Belgian-7 numbers.

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Mathematica

Extensions