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A066686 Array T(i,j) read by antidiagonals, where T(i,j) is the concatenation of i and j (1<=i, 1<=j).

%I A066686 #18 Nov 21 2021 14:05:19
%S A066686 11,12,21,13,22,31,14,23,32,41,15,24,33,42,51,16,25,34,43,52,61,17,26,
%T A066686 35,44,53,62,71,18,27,36,45,54,63,72,81,19,28,37,46,55,64,73,82,91,
%U A066686 110,29,38,47,56,65,74,83,92,101,111,210,39,48,57,66,75,84,93,102,111
%N A066686 Array T(i,j) read by antidiagonals, where T(i,j) is the concatenation of i and j (1<=i, 1<=j).
%C A066686 The element at T(i,j) is the {(i+j-1)(i+j-2)/2 + i}-th element read in the sequence.
%H A066686 Alexander Bogomolny, <a href="http://www.cut-the-knot.org/do_you_know/numbers.shtml">What is a number?</a>
%H A066686 Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations [Of] Integer Sequences And Pairing Functions</a>, arXiv preprint arXiv:1212.2732 [math.CO], 2012.
%F A066686 T(i, j) = i*10^A055642(i) + j. - _Michael S. Branicky_, Nov 21 2021
%e A066686 The array begins
%e A066686 11 12 13 14 15 16 17 18 19 110 ...
%e A066686 21 22 23 24 25 26 27 28 29 210 ...
%e A066686 31 32 33 34 35 36 37 38 39 310 ...
%e A066686 41 42 43 44 45 46 47 48 49 410 ...
%t A066686 a = {}; Do[ a = Append[a, ToExpression[ StringJoin[ ToString[k], ToString[n - k]]]], {n, 2, 13}, {k, 1, n - 1} ]; a
%o A066686 (Python)
%o A066686 def T(i, j): return int(str(i) + str(j))
%o A066686 def auptodiag(maxd):
%o A066686     return [T(i, d+1-i) for d in range(1, maxd+1) for i in range(1, d+1)]
%o A066686 print(auptodiag(12)) # _Michael S. Branicky_, Nov 21 2021
%Y A066686 Cf. A055642, A067574, A084854.
%K A066686 easy,nonn,tabl,base
%O A066686 1,1
%A A066686 _Robert G. Wilson v_, Jan 11 2002