A259443 The position of the first occurrence in the decimal expansion of Pi of n identical digits.

1, 3, 10, 24, 25, 27, 43, 45, 55, 58, 62, 79, 80, 100, 107, 113, 124, 134, 147, 150, 152, 161, 171, 186, 197, 204, 205, 222, 228, 233, 236, 255, 267, 273, 278, 293, 296, 303, 321, 334, 337, 354, 373, 380, 386, 392, 400, 432, 437, 438, 442, 445, 446, 471, 483, 490, 494, 495, 499

Offset

1,2

Comments

A test for normality.

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..1000

Formula

a(n) ~ 10*n and a(n-1) < a(n).

a(10) = 58, a(100) = 882, a(1000) = 9619, a(10000) = 98564, a(100000) = 996482.

Example

a(2) = 3 since the digit 1 occurs twice by the third place in the decimal expansion of Pi, i.e., "141".
a(3) = 10 since the digit 5 occurs three times by the tenth place in the decimal expansion of Pi, i.e., "1415926535".

Mathematica

pi3 = RealDigits[Pi - 3, 10, 1000][[1]]; f[n_] := f[n] = Block[{k = f[n - 1] + 1}, While[ Max[ Transpose[ Tally[ Take[pi3, k]]][[2]]] != n, k++]; k]; f[0] = 0; Array[f, 60]

Crossrefs

Cf. A000796, A159345.

Sequence in context: A041327 A231116 A272953 * A293405 A029880 A144413

Adjacent sequences: A259440 A259441 A259442 * A259444 A259445 A259446

Keyword

base,easy,nonn

Author

Douglas Boffey and Robert G. Wilson v, Jun 27 2015

Status

approved