A392937 Square array T, read by ascending antidiagonals, where T(n,k) (n, k >= 1) denotes the smallest position at which a length-n block of digits starting at position k reappears in the decimal expansion of Pi.

10, 138, 4, 2121, 104, 20, 3497, 296, 37, 38, 88009, 6956, 393, 315, 9, 176452, 6956, 5799, 731, 62, 13, 25198141, 821583, 81379, 9978, 62, 63, 17, 50366473, 1457056, 668834, 16630, 16631, 1475, 22, 21, 1660042752, 98863973, 3008601, 3008602, 638163, 4705, 1560, 109, 11

Offset

1,1

Comments

For n < 9 and k < 9, T(n,k) < 10^(n+1).

Links

Table of n, a(n) for n=1..45.

Example

T(1,1) = A065593(1) = 10, because 10 is the smallest position at which a length-1 block of digits starting at position 1, namely 3, reappears in the decimal expansion of Pi (A000796).
T(2,3) = 37, because 37 is the smallest position at which a length-2 block of digits starting at position 3, namely 41, reappears in the decimal expansion of Pi (A000796).
Top left square array begins at T(1,1):
  10, 4, 20, 38, 9, 13, 17;
  138, 104, 37, 315, 62, 63, 22;
  2121, 296, 393, 731, 62, 1475, 1560;
  3497, 6956, 5799, 9978, 16631, 4705, 8076;
  88009, 6956, 81379, 16630, 638163, 31201, 237173;
  176452, 821583, 668834, 3008602, 987243, 514859, 351254;
  25198141, 1457056, 3008601, 13557735, 6936672, 1559937, 38766787;

Crossrefs

Cf. A000796, A065593 (column 1), A094580 (row 1), A094582.

Sequence in context: A371394 A230344 A348137 * A318594 A065593 A362515

Adjacent sequences: A392934 A392935 A392936 * A392938 A392939 A392940

Keyword

nonn,base,tabl

Author

Jean-Marc Rebert, Apr 04 2026

Status

approved