A093846 Triangle read by rows: T(n, k) = 10^(n-1) - 1 + k*floor(9*10^(n-1)/n), for 1 <= k <= n.

9, 54, 99, 399, 699, 999, 3249, 5499, 7749, 9999, 27999, 45999, 63999, 81999, 99999, 249999, 399999, 549999, 699999, 849999, 999999, 2285713, 3571427, 4857141, 6142855, 7428569, 8714283, 9999997, 21249999, 32499999, 43749999, 54999999, 66249999, 77499999, 88749999, 99999999

Offset: 1

Author

Amarnath Murthy, Apr 18 2004

Keywords

• base
• easy
• less
• nonn
• tabl

Comments

10^(n-1)-1 and the n-th row are n+1 numbers in arithmetic progression and the common difference is the largest such that a(n, n) has n digits. This common difference equals A061772(n).

Examples

			Triangle begins:
     9;
    54,   99;
   399,  699,  999;
  3249, 5499, 7749, 9999;
  ...
		

Links

• G. C. Greubel, Rows n = 1..100 of triangle, flattened

Crossrefs

Cf. A061772, A093847, A093849, A093850.

Programs

Magma

[[10^(n-1) -1 +k*Floor(9*10^(n-1)/n): k in [1..n]]: n in [1..8]]; // G. C. Greubel, Mar 22 2019

Maple

A093846 := proc(n,k) RETURN (10^(n-1)-1+k*floor(9*(10^(n-1)/n))); end; for n from 1 to 10 do for k from 1 to n do printf("%d,",A093846(n,k)); od; od; # R. J. Mathar, Jun 23 2006

Mathematica

Table[# -1 +k Floor[9 #/n] &[10^(n-1)], {n, 8}, {k, n}]//Flatten (* Michael De Vlieger, Jul 18 2016 *)

PARI

{T(n,k) = 10^(n-1) -1 +k*floor(9*10^(n-1)/n)}; \\ G. C. Greubel, Mar 22 2019

Sage

[[10^(n-1) -1 +k*floor(9*10^(n-1)/n) for k in (1..n)] for n in (1..8)] # G. C. Greubel, Mar 22 2019

Extensions

Corrected and extended by R. J. Mathar, Jun 23 2006

Edited by David Wasserman, Mar 26 2007