A053747 -id:A053747 - cp's OEIS frontend

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

Clark Kimberling, Dec 17 2021

Every positive integer occurs exactly once.

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

			(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

Index entries for sequences that are permutations of the natural numbers

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

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 *)

A346122 n times the n-th digit of the decimal expansion of Pi.

Original entry on oeis.org

3, 2, 12, 4, 25, 54, 14, 48, 45, 30, 55, 96, 117, 98, 135, 48, 34, 54, 152, 80, 126, 44, 138, 96, 75, 78, 216, 84, 58, 210, 279, 160, 0, 68, 280, 288, 148, 38, 351, 280, 41, 252, 387, 132, 405, 414, 141, 336, 245, 50, 0, 260, 424, 108, 0, 504, 399, 232, 531

Offset: 1

Harvey P. Dale, Jul 05 2021

			The first  digit of the decimal expansion of Pi is 3, so a(1) = 1*3 = 3.
The second digit of the decimal expansion of Pi is 1, so a(2) = 2*1 = 2.
The third  digit of the decimal expansion of Pi is 4, so a(3) = 3*4 = 12.

Index entries for sequences related to the number Pi

Cf. A000796, A014976 (zeros), A053745 (fixed points).

Cf. A053746, A053747, A053748, A053749, A053750, A053751, A053752, A053753.

Module[{nn=120,pid},pid=RealDigits[Pi,10,nn][[1]];Table[n pid[[n]],{n,nn}]]

from sympy import S
def aupton(terms):
    digits_of_pi = "0" + str(S.Pi.n(terms+1)).replace('.', '')
    return [n*int(digits_of_pi[n]) for n in range(1, terms+1)]
print(aupton(59)) # Michael S. Branicky, Jul 08 2021

cp's OEIS Frontend

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

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