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

Author

Felix Fröhlich, Apr 01 2015

Keywords

• nonn
• base
• tabl

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, ...

...

Examples

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

Links

• Robert G. Wilson v, Table of n, a(n) for n = 0..1000
• D. G. Andersen, The Pi-Search Page

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).

Programs

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 *)

Extensions

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