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

1,2

Comments

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

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.

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)

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A081552, A081553.

Sequence in context: A332795 A303605 A266946 * A257831 A007088 A115848

Adjacent sequences: A081548 A081549 A081550 * A081552 A081553 A081554

Keyword

base,easy,nonn,tabl

Author

Amarnath Murthy, Apr 01 2003

Extensions

More terms from Philippe Deléham, Mar 28 2009

Status

approved