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approved
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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.
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Triangle , read by rows , in which the n-th row contains n smallest n-digit numbers.
G. C. Greubel, <a href="/A081551/b081551.txt">Rows n = 0..50 of the triangle, flattened</a>
From Franz Vrabec, Jul 28 2019: (Start)
T(n, k) = 10^(n-1) + k - 1.
T(n,k) = 10^(n-1)+k-1. But considered as As a one-dimensional sequence, : a(n) = 10^m + n - (m^2 + m + 2)/2 where m = floor((-1 + sqrt(8*n-7))/2). - _Franz Vrabec_, Jul 28 2019(End)
1; 10,11; 100,101,102; 1000,1001,1002,1003; ...
Triangle begins as:
1;
10, 11;
100, 101, 102;
1000, 1001, 1002, 1003;
10000, 10001, 10002, 10003, 10004;
100000, 100001, 100002, 100003, 100004, 100005;
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
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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
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approved
editing
proposed
T(n,k) = 10^(n-1)+k-1. But considered as one-dimensional sequence, a(n) = 10^m+n-(m^2+m+2)/2 where m = floor((-1+sqrt(8*n-7))/2). - Franz Vrabec, Jul 28 2019