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A081551
Triangle, read by rows, in which the n-th row contains n smallest n-digit numbers.
3
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
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
Sequence in context: A332795 A303605 A266946 * A257831 A007088 A115848
KEYWORD
base,easy,nonn,tabl
AUTHOR
Amarnath Murthy, Apr 01 2003
EXTENSIONS
More terms from Philippe Deléham, Mar 28 2009
STATUS
approved