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

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, 24, 9, 8, 98, 95, 54, 25, 37, 11, 21, 14, 107, 96, 64, 26, 58, 32, 23, 30, 12, 117, 104, 74, 28, 60, 49, 42, 40, 19, 6

Offset: 0

Author

Clark Kimberling, Dec 17 2021

Keywords

• nonn
• tabf

Comments

Every positive integer occurs exactly once.

It is assumed that each digit occurs infinitely many times in A000796.

Examples

			(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.
Corner:
  33, 51, 55, 66, 72, 78, 86, 98,  107,  117, 122, ... A014976
   2,  4, 38, 41, 50, 69, 95, 96,  104,  111, 139, ... A053745
   7, 17, 22, 29, 34, 54, 64, 74,   77,   84,  90, ... A053746
   1, 10, 16, 18, 25, 26, 28, 44,   47,   65,  87, ... A053747
   3, 20, 24, 37, 58, 60, 61, 71,   88,   93, 105, ... A053748
   5,  9, 11, 32, 49, 52, 62, 91,  110,  131, 132, ... A053749
   8, 21, 23, 42, 70, 73, 76, 83,   99,  109, 118, ... A053750
  14, 30, 40, 48, 57, 67, 97, 100, 121,  140, 157, ... A053751
  12, 19, 27, 35, 36, 53, 68, 75,   79,   82,  85, ... A053752
   6, 13, 15, 31, 39, 43, 45, 46,   56,   59,  63, ... A053753
		

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000796, A014976, A053745-A053753, A032445 (includes column 1).

Programs

Mathematica

r = RealDigits[Pi, 10, 200][[1]]
t = Table[Flatten[Position[r, n]], {n, 0, 9}]
TableForm[t]  (* A349551 array *)
Flatten[Table[t[[n - k + 1, k]], {n, 10}, {k, n, 1, -1}]] (* A349551 sequence *)