A262437 Triangle T(n,k): write n in base 16, reverse order of digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 1, 10, 1, 11, 1, 12, 1, 13, 1, 14, 1, 15, 1, 0, 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7, 2, 8, 2, 9, 2, 10, 2, 11, 2, 12, 2, 13, 2, 14, 2, 15, 2

Offset: 0

Author

Reinhard Zumkeller, Sep 22 2015

Keywords

• nonn
• tabf
• base

Comments

Sum(T(n,k)*16^k : k = 0..A262438(n)-1) = n.

Examples

			.   n | HEX | T(n,*)        n | HEX | T(n,*)        n | HEX | T(n,*)
. ----+-----+--------     ----+-----+--------     ----+-----+--------
.   0 |   0 |  [0]         24 |  18 |  [8,1]       48 |  30 |  [0,3]
.   1 |   1 |  [1]         25 |  19 |  [9,1]       49 |  31 |  [1,3]
.   2 |   2 |  [2]         26 |  1A |  [10,1]      50 |  32 |  [2,3]
.   3 |   3 |  [3]         27 |  1B |  [11,1]      51 |  33 |  [3,3]
.   4 |   4 |  [4]         28 |  1C |  [12,1]      52 |  34 |  [4,3]
.   5 |   5 |  [5]         29 |  1D |  [13,1]      53 |  35 |  [5,3]
.   6 |   6 |  [6]         30 |  1E |  [14,1]      54 |  36 |  [6,3]
.   7 |   7 |  [7]         31 |  1F |  [15,1]      55 |  37 |  [7,3]
.   8 |   8 |  [8]         32 |  20 |  [0,2]       56 |  38 |  [8,3]
.   9 |   9 |  [9]         33 |  21 |  [1,2]       57 |  39 |  [9,3]
.  10 |   A |  [10]        34 |  22 |  [2,2]       58 |  3A |  [10,3]
.  11 |   B |  [11]        35 |  23 |  [3,2]       59 |  3B |  [11,3]
.  12 |   C |  [12]        36 |  24 |  [4,2]       60 |  3C |  [12,3]
.  13 |   D |  [13]        37 |  25 |  [5,2]       61 |  3D |  [13,3]
.  14 |   E |  [14]        38 |  26 |  [6,2]       62 |  3E |  [14,3]
.  15 |   F |  [15]        39 |  27 |  [7,2]       63 |  3F |  [15,3]
.  16 |  10 |  [0,1]       40 |  28 |  [8,2]       64 |  40 |  [0,4]
.  17 |  11 |  [1,1]       41 |  29 |  [9,2]       65 |  41 |  [1,4]
.  18 |  12 |  [2,1]       42 |  2A |  [10,2]      66 |  42 |  [2,4]
.  19 |  13 |  [3,1]       43 |  2B |  [11,2]      67 |  43 |  [3,4]
.  20 |  14 |  [4,1]       44 |  2C |  [12,2]      68 |  44 |  [4,4]
.  21 |  15 |  [5,1]       45 |  2D |  [13,2]      69 |  45 |  [5,4]
.  22 |  16 |  [6,1]       46 |  2E |  [14,2]      70 |  46 |  [6,4]
.  23 |  17 |  [7,1]       47 |  2F |  [15,2]      71 |  47 |  [7,4]
.  24 |  18 |  [8,1]       48 |  30 |  [0,3]       72 |  48 |  [8,4]  .
		

Links

• Reinhard Zumkeller, Rows n = 0..10000 of triangle, flattened
• Eric Weisstein's World of Mathematics, Hexadecimal
• Wikipedia, Hexadecimal

Crossrefs

Cf. A001025, A262438 (row lengths), A030308 (binary), A030341 (ternary), A031298 (decimal).

Programs

Haskell

a262437 n k = a262437_tabf !! n !! k
a262437_row n = a262437_tabf !! n
a262437_tabf = iterate succ [0] where
   succ []      = [1]
   succ (15:hs) = 0 : succ hs
   succ (h:hs)  = (h + 1) : hs