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A273825 Table read by rows: the n-th row is the list of numbers diagonally up and to the left of n in the natural numbers read by antidiagonals.

%I A273825 #20 Jun 30 2016 02:01:56
%S A273825 1,2,3,4,5,1,6,7,8,2,9,3,10,11,12,4,13,5,1,14,6,15,16,17,7,18,8,2,19,
%T A273825 9,3,20,10,21,22,23,11,24,12,4,25,13,5,1,26,14,6,27,15,28,29,30,16,31,
%U A273825 17,7,32,18,8,2,33,19,9,3,34,20,10,35,21,36,37,38,22
%N A273825 Table read by rows: the n-th row is the list of numbers diagonally up and to the left of n in the natural numbers read by antidiagonals.
%H A273825 Peter Kagey, <a href="/A273825/b273825.txt">Table of n, a(n) for n = 1..10000</a>
%e A273825 A000027 read by antidiagonals is:
%e A273825 1 2 4 7
%e A273825 3 5 8
%e A273825 6 9
%e A273825 ...
%e A273825 Thus:
%e A273825 Row 1: []
%e A273825 Row 2: []
%e A273825 Row 3: []
%e A273825 Row 4: []
%e A273825 Row 5: [1]
%e A273825 Row 6: []
%e A273825 Row 7: []
%e A273825 Row 8: [2]
%e A273825 Row 9: [3]
%t A273825 nn = 58; t = Table[(n^2 - n)/2 + Accumulate@ Range[n - 1, Ceiling[(Sqrt[9 + 8 nn] - 3)/2]] + 1, {n, Ceiling[(Sqrt[9 + 8 nn] - 3)/2] + 1}]; Table[Rest@ Map[t[[#1, #2]] & @@ # &, Most@ NestWhileList[# - 1 &, #, ! MemberQ[#, 0] &]] &@ First@ Position[t, n], {n, nn}] // Flatten (* _Michael De Vlieger_, Jun 29 2016 *)
%o A273825 (Haskell)
%o A273825 a273825 n = genericIndex a273825_list (n - 1)
%o A273825 a273825_list = concatMap a273825_row [1..]
%o A273825 a273825_tabf = map a273825_row [1..]
%o A273825 a273825_row n
%o A273825   | a_i == 0  = []
%o A273825   | otherwise = a_i : a273825_row a_i where
%o A273825     a_i = a271439 $ a271439 (n - 1)
%Y A273825 Cf. A000027, A269526, A271439, A273823, A273824, A274079, A274080.
%K A273825 nonn,tabf
%O A273825 1,2
%A A273825 _Peter Kagey_, Jun 08 2016