

A259443


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


1



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
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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(n1) < 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



