A081551 Triangle, read by rows, in which the n-th row contains n smallest n-digit numbers.

1, 10, 11, 100, 101, 102, 1000, 1001, 1002, 1003, 10000, 10001, 10002, 10003, 10004, 100000, 100001, 100002, 100003, 100004, 100005, 1000000, 1000001, 1000002, 1000003, 1000004, 1000005, 1000006, 10000000, 10000001, 10000002, 10000003, 10000004, 10000005, 10000006, 10000007

Offset: 1

Author

Amarnath Murthy, Apr 01 2003

Keywords

• base
• easy
• nonn
• tabl

Comments

This sequence has asymptotic density 0 and Banach density 1 (see Mithun Kumar Das reference p.2). - Franz Vrabec, Jul 28 2019

Examples

			Triangle begins as:
       1;
      10,     11;
     100,    101,    102;
    1000,   1001,   1002,   1003;
   10000,  10001,  10002,  10003,  10004;
  100000, 100001, 100002, 100003, 100004, 100005;
		

Links

• G. C. Greubel, Rows n = 0..50 of the triangle, flattened
• Mithun Kumar Das, Pramod Eyyunni, and Bhuwanesh Rao Patil, Sparse subsets of the natural numbers and Euler's totient function, arXiv:1907.09847v1 [math.NT] 23 Jul 2019.

Crossrefs

Cf. A081552, A081553.

Programs

Mathematica

Table[10^(n-1) +k-1, {n,12}, {k,n}]//Flatten (* G. C. Greubel, May 27 2021 *)

Sage

flatten([[10^(n-1) +k-1 for k in (1..n)] for n in (1..12)]) # G. C. Greubel, May 27 2021

Formula

From Franz Vrabec, Jul 28 2019: (Start)

T(n, k) = 10^(n-1) + k - 1.

As a one-dimensional sequence: a(n) = 10^m + n - (m^2 + m + 2)/2 where m = floor((-1 + sqrt(8*n-7))/2). (End)

Extensions

More terms from Philippe Deléham, Mar 28 2009