A262437 - OEIS

%I #5 Sep 23 2015 04:45:21

%S 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,

%T 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,

%U 7,2,8,2,9,2,10,2,11,2,12,2,13,2,14,2,15,2

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

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

%H Reinhard Zumkeller, <a href="/A262437/b262437.txt">Rows n = 0..10000 of triangle, flattened</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Hexadecimal.html">Hexadecimal</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Hexadecimal">Hexadecimal</a>

%e .   n | HEX | T(n,*)        n | HEX | T(n,*)        n | HEX | T(n,*)

%e . ----+-----+--------     ----+-----+--------     ----+-----+--------

%e .   0 |   0 |  [0]         24 |  18 |  [8,1]       48 |  30 |  [0,3]

%e .   1 |   1 |  [1]         25 |  19 |  [9,1]       49 |  31 |  [1,3]

%e .   2 |   2 |  [2]         26 |  1A |  [10,1]      50 |  32 |  [2,3]

%e .   3 |   3 |  [3]         27 |  1B |  [11,1]      51 |  33 |  [3,3]

%e .   4 |   4 |  [4]         28 |  1C |  [12,1]      52 |  34 |  [4,3]

%e .   5 |   5 |  [5]         29 |  1D |  [13,1]      53 |  35 |  [5,3]

%e .   6 |   6 |  [6]         30 |  1E |  [14,1]      54 |  36 |  [6,3]

%e .   7 |   7 |  [7]         31 |  1F |  [15,1]      55 |  37 |  [7,3]

%e .   8 |   8 |  [8]         32 |  20 |  [0,2]       56 |  38 |  [8,3]

%e .   9 |   9 |  [9]         33 |  21 |  [1,2]       57 |  39 |  [9,3]

%e .  10 |   A |  [10]        34 |  22 |  [2,2]       58 |  3A |  [10,3]

%e .  11 |   B |  [11]        35 |  23 |  [3,2]       59 |  3B |  [11,3]

%e .  12 |   C |  [12]        36 |  24 |  [4,2]       60 |  3C |  [12,3]

%e .  13 |   D |  [13]        37 |  25 |  [5,2]       61 |  3D |  [13,3]

%e .  14 |   E |  [14]        38 |  26 |  [6,2]       62 |  3E |  [14,3]

%e .  15 |   F |  [15]        39 |  27 |  [7,2]       63 |  3F |  [15,3]

%e .  16 |  10 |  [0,1]       40 |  28 |  [8,2]       64 |  40 |  [0,4]

%e .  17 |  11 |  [1,1]       41 |  29 |  [9,2]       65 |  41 |  [1,4]

%e .  18 |  12 |  [2,1]       42 |  2A |  [10,2]      66 |  42 |  [2,4]

%e .  19 |  13 |  [3,1]       43 |  2B |  [11,2]      67 |  43 |  [3,4]

%e .  20 |  14 |  [4,1]       44 |  2C |  [12,2]      68 |  44 |  [4,4]

%e .  21 |  15 |  [5,1]       45 |  2D |  [13,2]      69 |  45 |  [5,4]

%e .  22 |  16 |  [6,1]       46 |  2E |  [14,2]      70 |  46 |  [6,4]

%e .  23 |  17 |  [7,1]       47 |  2F |  [15,2]      71 |  47 |  [7,4]

%e .  24 |  18 |  [8,1]       48 |  30 |  [0,3]       72 |  48 |  [8,4]  .

%o (Haskell)

%o a262437 n k = a262437_tabf !! n !! k

%o a262437_row n = a262437_tabf !! n

%o a262437_tabf = iterate succ [0] where

%o    succ []      = [1]

%o    succ (15:hs) = 0 : succ hs

%o    succ (h:hs)  = (h + 1) : hs

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

%K nonn,tabf,base

%O 0,3

%A _Reinhard Zumkeller_, Sep 22 2015