A256521 Table T(n, k) of positions p[i] where number n occurs after the decimal point in the decimal expansion of Pi, read by antidiagonals.

32, 50, 1, 54, 3, 6, 65, 37, 16, 9, 71, 40, 21, 15, 2, 77, 49, 28, 17, 19, 4, 85, 68, 33, 24, 23, 8, 7, 97, 94, 53, 25, 36, 10, 20, 13, 106, 95, 63, 27, 57, 31, 22, 29, 11, 116, 103, 73, 43, 59, 48, 41, 39, 18, 5, 121, 110, 76, 46, 60, 51, 69, 47, 26, 12, 49, 128, 138, 83, 64, 70, 61, 72, 56, 34, 14, 163, 94

Offset

0,1

Comments

Table T(n, k) starts:

n = 0: 32, 50, 54, 65, 71, 77, 85, 97, 106, 116, ...

n = 1: 1, 3, 37, 40, 49, 68, 94, 95, 103, 110, ...

n = 2: 6, 16, 21, 28, 33, 53, 63, 73, 76, 83, ...

n = 3: 9, 15, 17, 24, 25, 27, 43, 46, 64, 86, ...

n = 4: 2, 19, 23, 36, 57, 59, 60, 70, 87, 92, ...

n = 5: 4, 8, 10, 31, 48, 51, 61, 90, 109, 130, ...

n = 6: 7, 20, 22, 41, 69, 72, 75, 82, 98, 108, ...

n = 7: 13, 29, 39, 47, 56, 66, 96, 99, 120, 139, ...

n = 8: 11, 18, 26, 34, 35, 52, 67, 74, 78, 81, ...

n = 9: 5, 12, 14, 30, 38, 42, 44, 45, 55, 58, ...

n = 10: 49, 163, 175, 206, 269, 442, 681, 780, 852, 854, ...

...

Links

Robert G. Wilson v, Table of n, a(n) for n = 0..1000

D. G. Andersen, The Pi-Search Page

Example

T(6, 4) = 41, since the fourth occurrence of 6 in the decimal expansion of Pi is at position 41.

Mathematica

spi = StringDrop[ ToString[ N[ Pi, 1000]], 2]; t[n_, k_] := StringPosition[ spi, ToString[n], k][[-1, 1]]; Table[ t[n - k, k], {n, 0, 12}, {k, n, 1, -1}] // Flatten (* Robert G. Wilson v, Apr 07 2015 *)

Crossrefs

Cf. A000796 (Pi), A014777 (first column).

Cf. A037008, A037000, A037001, A037002, A037003 (0th to 4th row).

Cf. A037004, A037005, A036974, A037006, A037007 (5th to 9th row).

Sequence in context: A066472 A140172 A259765 * A037008 A316943 A099048

Adjacent sequences: A256518 A256519 A256520 * A256522 A256523 A256524

Keyword

nonn,base,tabl

Author

Felix Fröhlich, Apr 01 2015

Extensions

More terms from Robert G. Wilson v, Apr 07 2015

Status

approved