A081553 -id:A081553 - cp's OEIS frontend

A081552 Leading terms of rows in A081551.

1, 11, 102, 1003, 10004, 100005, 1000006, 10000007, 100000008, 1000000009, 10000000010, 100000000011, 1000000000012, 10000000000013, 100000000000014, 1000000000000015, 10000000000000016, 100000000000000017, 1000000000000000018

Offset: 1

Amarnath Murthy, Apr 01 2003

More generally, a(n) = B^K + n; K = floor(log_B a(n-1)) + 1. This sequence has B=10, a(0)=1; A006127 has B=2, a(0)=1; A052944 has B=2, a(0)=2; A104743 has B=3, a(0)=1; A104745 has B=5, a(0)=1. - Ctibor O. Zizka, Mar 22 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..300
Index entries for linear recurrences with constant coefficients, signature (12,-21,10).

Cf. A011557, A081551, A081553, A085952 (first differences, after n=2).

[10^(n-1)+n-1: n in [1..20]]; // Vincenzo Librandi, Jun 16 2013

I:=[1, 11, 102]; [n le 3 select I[n] else 12*Self(n-1)-21*Self(n-2)+10*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 16 2013

seq(10^(n-1) +n-1, n=1..40); # G. C. Greubel, May 27 2021

Table[10^(n-1) +n-1, {n,30}] (* or *) CoefficientList[Series[(1-x-9x^2)/((1-10x)(1-x)^2), {x, 0, 30}], x]  (* Vincenzo Librandi, Jun 16 2013 *)

[10^(n-1) +n-1 for n in (1..40)] # G. C. Greubel, May 27 2021

a(n) = 10^(n-1) + n-1.
G.f.: x*(1 -x -9*x^2)/((1-10*x)*(1-x)^2). - Vincenzo Librandi, Jun 16 2013
a(n) = 12*a(n-1) -21*a(n-2) +10*a(n-3). - Vincenzo Librandi, Jun 16 2013
E.g.f.: (1/10)*(9 - 10*(1-x)*exp(x) + exp(10*x)). - G. C. Greubel, May 27 2021

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

Original entry on oeis.org

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

Amarnath Murthy, Apr 01 2003

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

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

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.

Cf. A081552, A081553.

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

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

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)

More terms from Philippe Deléham, Mar 28 2009

cp's OEIS Frontend

A081552 Leading terms of rows in A081551.

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