A162711 Triangle read by rows: T(n,k) = value of the string of length k beginning at position n in the concatenation of natural numbers in decimal representation, 1<=k<=n.

1, 2, 23, 3, 34, 345, 4, 45, 456, 4567, 5, 56, 567, 5678, 56789, 6, 67, 678, 6789, 67891, 678910, 7, 78, 789, 7891, 78910, 789101, 7891011, 8, 89, 891, 8910, 89101, 891011, 8910111, 89101112, 9, 91, 910, 9101, 91011, 910111, 9101112, 91011121, 910111213

Offset: 1

Author

Reinhard Zumkeller, Jul 11 2009

Keywords

• base
• nonn
• tabl

Comments

A055642(T(n,k)) <= k;

T(n,1)=A007376(n); T(n,k)=10*T(n,k-1)+A007376(k), 1

T(n,2)=A136414(n) for n>1.

Links

• Reinhard Zumkeller, Rows n = 1..125 of table, flattened

Crossrefs

Cf. A224841 where n is the position of the last digit of the string.

Programs

Haskell

import Data.List (inits, tails)
a162711 n k = a162711_tabl !! (n-1) !! (k-1)
a162711_row n = a162711_tabl !! (n-1)
a162711_tabl = map (map (read . concatMap show) . tail . inits) $
               zipWith take [1..] $ tails a007376_list :: [[Integer]]
-- Reinhard Zumkeller, Nov 11 2013

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