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