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

Author

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

Keywords

• base
• easy
• nonn

Comments

A test for normality.

Examples

			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".
		

Links

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

Crossrefs

Cf. A000796, A159345.

Programs

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]

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.