cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

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

Original entry on oeis.org

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

Views

Author

Amarnath Murthy, Apr 18 2004

Keywords

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

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

A093852 a(n) = 10^(n-1) - 1 + n*floor(9*10^(n-1)/(n+1)).

Original entry on oeis.org

4, 69, 774, 8199, 84999, 871425, 8874999, 89999999, 909999999, 9181818179, 92499999999, 930769230759, 9357142857140, 93999999999999, 943749999999999, 9470588235294111, 94999999999999999, 952631578947368403, 9549999999999999999, 95714285714285714279
Offset: 1

Views

Author

Amarnath Murthy, Apr 18 2004

Keywords

Comments

This sequence is the main diagonal of A093850.

Examples

			n-th row of the following 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.
Given the triangle defined in A093850:
...4;
..39   69;
.324  549  774;
2799 4599 6399 8199.....
then this sequence is the leading diagonal.

Links

Crossrefs

Cf. A093846, A093847, A061772, A093450, A072875.

Programs

  • Magma
    [10^(n-1) -1 +n*Floor(9*10^(n-1)/(n+1)): n in [1..25]]; // G. C. Greubel, Mar 21 2019
  • Maple
    A093852 := proc(n)
        r := n ;
        10^(n-1)-1+r*floor(9*10^(n-1)/(n+1)) ;
end proc:
seq(A093852(n),n=1..50) ; # R. J. Mathar, Oct 01 2011
  • Mathematica
    Table[10^(n-1) -1 +n*Floor[9*10^(n-1)/(n+1)], {n,25}] (* G. C. Greubel, Mar 21 2019 *)
  • PARI
    {a(n) = 10^(n-1) -1 +n*floor(9*10^(n-1)/(n+1))}; \\ G. C. Greubel, Mar 21 2019
  • Sage
    [10^(n-1) -1 +n*floor(9*10^(n-1)/(n+1)) for n in (1..25)] # G. C. Greubel, Mar 21 2019
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.