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A349551 Rectangular array with ten rows, read by falling antidiagonals: row k gives positions of k in the decimal expansion (A000796) of Pi.

%I A349551 #16 Dec 17 2021 20:33:41
%S A349551 33,51,2,55,4,7,66,38,17,1,72,41,22,10,3,78,50,29,16,20,5,86,69,34,18,
%T A349551 24,9,8,98,95,54,25,37,11,21,14,107,96,64,26,58,32,23,30,12,117,104,
%U A349551 74,28,60,49,42,40,19,6
%N A349551 Rectangular array with ten rows, read by falling antidiagonals: row k gives positions of k in the decimal expansion (A000796) of Pi.
%C A349551 Every positive integer occurs exactly once.
%C A349551 It is assumed that each digit occurs infinitely many times in A000796.
%H A349551 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A349551 (Base-10 digits of Pi) = (3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8, 4, 6, 2, 6, 4, 3, 3, 8, 3, 2, 7, 9, 5, 0, ...); the position of the first 0 is 33, so the first term in row 0 is 33.
%e A349551 Corner:
%e A349551   33, 51, 55, 66, 72, 78, 86, 98,  107,  117, 122, ... A014976
%e A349551    2,  4, 38, 41, 50, 69, 95, 96,  104,  111, 139, ... A053745
%e A349551    7, 17, 22, 29, 34, 54, 64, 74,   77,   84,  90, ... A053746
%e A349551    1, 10, 16, 18, 25, 26, 28, 44,   47,   65,  87, ... A053747
%e A349551    3, 20, 24, 37, 58, 60, 61, 71,   88,   93, 105, ... A053748
%e A349551    5,  9, 11, 32, 49, 52, 62, 91,  110,  131, 132, ... A053749
%e A349551    8, 21, 23, 42, 70, 73, 76, 83,   99,  109, 118, ... A053750
%e A349551   14, 30, 40, 48, 57, 67, 97, 100, 121,  140, 157, ... A053751
%e A349551   12, 19, 27, 35, 36, 53, 68, 75,   79,   82,  85, ... A053752
%e A349551    6, 13, 15, 31, 39, 43, 45, 46,   56,   59,  63, ... A053753
%t A349551 r = RealDigits[Pi, 10, 200][[1]]
%t A349551 t = Table[Flatten[Position[r, n]], {n, 0, 9}]
%t A349551 TableForm[t]  (* A349551 array *)
%t A349551 Flatten[Table[t[[n - k + 1, k]], {n, 10}, {k, n, 1, -1}]] (* A349551 sequence *)
%Y A349551 Cf. A000796, A014976, A053745-A053753, A032445 (includes column 1).
%K A349551 nonn,tabf
%O A349551 0,1
%A A349551 _Clark Kimberling_, Dec 17 2021