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

%I A081551 #23 May 29 2021 20:05:01
%S A081551 1,10,11,100,101,102,1000,1001,1002,1003,10000,10001,10002,10003,
%T A081551 10004,100000,100001,100002,100003,100004,100005,1000000,1000001,
%U A081551 1000002,1000003,1000004,1000005,1000006,10000000,10000001,10000002,10000003,10000004,10000005,10000006,10000007
%N A081551 Triangle, read by rows, in which the n-th row contains n smallest n-digit numbers.
%C A081551 This sequence has asymptotic density 0 and Banach density 1 (see Mithun Kumar Das reference p.2). - _Franz Vrabec_, Jul 28 2019
%H A081551 G. C. Greubel, <a href="/A081551/b081551.txt">Rows n = 0..50 of the triangle, flattened</a>
%H A081551 Mithun Kumar Das, Pramod Eyyunni, and Bhuwanesh Rao Patil, <a href="https://arxiv.org/abs/1907.09847">Sparse subsets of the natural numbers and Euler's totient function</a>, arXiv:1907.09847v1 [math.NT] 23 Jul 2019.
%F A081551 From _Franz Vrabec_, Jul 28 2019: (Start)
%F A081551 T(n, k) = 10^(n-1) + k - 1.
%F A081551 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)
%e A081551 Triangle begins as:
%e A081551        1;
%e A081551       10,     11;
%e A081551      100,    101,    102;
%e A081551     1000,   1001,   1002,   1003;
%e A081551    10000,  10001,  10002,  10003,  10004;
%e A081551   100000, 100001, 100002, 100003, 100004, 100005;
%t A081551 Table[10^(n-1) +k-1, {n,12}, {k,n}]//Flatten (* _G. C. Greubel_, May 27 2021 *)
%o A081551 (Sage) flatten([[10^(n-1) +k-1 for k in (1..n)] for n in (1..12)]) # _G. C. Greubel_, May 27 2021
%Y A081551 Cf. A081552, A081553.
%K A081551 base,easy,nonn,tabl
%O A081551 1,2
%A A081551 _Amarnath Murthy_, Apr 01 2003
%E A081551 More terms from _Philippe Deléham_, Mar 28 2009