A218978 Table read by rows: n-th row lists all distinct substrings of decimal representation of n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 10, 1, 11, 1, 2, 12, 1, 3, 13, 1, 4, 14, 1, 5, 15, 1, 6, 16, 1, 7, 17, 1, 8, 18, 1, 9, 19, 0, 2, 20, 1, 2, 21, 2, 22, 2, 3, 23, 2, 4, 24, 2, 5, 25, 2, 6, 26, 2, 7, 27, 2, 8, 28, 2, 9, 29, 0, 3, 30, 1, 3, 31, 2, 3, 32, 3

Offset: 0

Author

Reinhard Zumkeller, May 02 2015, Nov 10 2012

Keywords

• nonn
• base
• tabf
• look

Comments

A120004(n) = length of n-th row;

A154771(n) = sum of n-th row.

Examples

			Rows 100 .. 112:
.  100:  {0, 1, 10, 100},
.  101:  {0, 1, 10, 101},
.  102:  {0, 1, 2, 10, 102},
.  103:  {0, 1, 3, 10, 103},
.  104:  {0, 1, 4, 10, 104},
.  105:  {0, 1, 5, 10, 105},
.  106:  {0, 1, 6, 10, 106},
.  107:  {0, 1, 7, 10, 107},
.  108:  {0, 1, 8, 10, 108},
.  109:  {0, 1, 9, 10, 109},
.  110:  {0, 1, 10 ,11, 110},
.  111:  {1, 11, 111},
.  112:  {1, 2, 11, 12, 112}.
		

Links

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

Crossrefs

Cf. A031298, A219031 (squares in row), A262188 (palindromes in row).

Programs

Haskell

import Data.List (inits, tails, sort, nub, genericIndex)
a218978 n k = a218978_row n !! k
a218978_row n = genericIndex a218978_tabf n
a218978_tabf = map (sort . nub . map (foldr (\d v -> 10 * v + d) 0) .
                   concatMap (tail . inits) . tails) a031298_tabf
-- Reinhard Zumkeller, corrected: Sep 15 2015, May 02 2015, Nov 10 2012