A093850 Triangle T(n,k) = 10^(n-1) -1 + k*floor(9*10^(n-1)/(n+1)), with 1 <= r <= n, read by rows.

4, 39, 69, 324, 549, 774, 2799, 4599, 6399, 8199, 24999, 39999, 54999, 69999, 84999, 228570, 357141, 485712, 614283, 742854, 871425, 2124999, 3249999, 4374999, 5499999, 6624999, 7749999, 8874999, 19999999, 29999999, 39999999, 49999999, 59999999, 69999999, 79999999, 89999999

Offset: 1

Author

Amarnath Murthy, Apr 18 2004

Keywords

• easy
• nonn
• tabl
• base

Comments

The n-th row of this triangle contains n uniformly located n-digit numbers, i.e., n terms of an arithmetic progression with 10^(n-1)-1 as the term preceding the first term and (n+1)-th term is the largest possible n-digit term.

Starting with n=2, the n-th row of this triangle can be obtained by deleting the least significant digit, 9, from terms ending in 9 in the (n+1)-th row, and ignoring the main diagonal terms, of the triangle in A093846.

Floor(A093846(4,1)/10) = T(3,1) = 324, but floor(A093846(2,1)/10) = 5 and T(1,1) = 4, floor(A093846(7,1)/10) = 228571 and T(6,1) = 228570, etc. - Michael De Vlieger, Jul 18 2016

Examples

			Triangle begins with:
      4;
     39,    69;
    324,   549,   774;
   2799,  4599,  6399,  8199;
  24999, 39999, 54999, 69999, 84999;
  ....
		

Links

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

Crossrefs

Cf. A093846, A093847, A061772, A093451, A093552.

Cf. A093852.

Programs

Magma

[[10^(n-1) -1 +k*Floor(9*10^(n-1)/(n+1)): k in [1..n]]: n in [1..8]]; // G. C. Greubel, Mar 21 2019

Maple

A093850 := proc(n,r)
        10^(n-1)-1+r*floor(9*10^(n-1)/(n+1)) ;
end proc:
seq(seq(A093850(n,r),r=1..n),n=1..14) ; # R. J. Mathar, Sep 28 2011

Mathematica

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

PARI

{T(n,k) = 10^(n-1) -1 +k*floor(9*10^(n-1)/(n+1))}; \\ G. C. Greubel, Mar 21 2019

Sage

[[10^(n-1) -1 +k*floor(9*10^(n-1)/(n+1)) for k in (1..n)] for n in (1..8)] # G. C. Greubel, Mar 21 2019

Extensions

Second comment clarified by Michael De Vlieger, Jul 18 2016

Edited by G. C. Greubel, Mar 21 2019