A394265 - OEIS

%I #9 Mar 22 2026 17:50:52

%S 1,2,3,7,8,9,10,36,37,38,39,40,52,53,54,55,56,57,58,71,72,73,74,75,76,

%T 77,78,79,94,95,97,98,99,100,124,140,479,487,549,557,560,561,568,570,

%U 576,578,585,592,623,626,627,632,634,635,636,637,638,639,640,695

%N Positive integers k for which the Chebyshev distance between the vector of proportions of the first k decimal digits of Pi and the uniform distribution (1/10, ..., 1/10) sets a new minimum.

%C The corresponding sequences for bases 2, 3, 4, and 5 are finite, because each digit occurs equally many times among the first 4, 15, 4, and 75 digits of Pi in base 2 (see A039624), 3 (see A278977, A278978, and A278979), 4, and 5 respectively:

%C   base 2: 1, 3, 4;

%C   base 3: 1, 2, 6, 11, 12, 13, 14, 15;

%C   base 4: 1, 2, 4;

%C   base 5: 1, 2, 7, 8, 9, 22, 23, 26, 30, 43, 46, 47, 53, 54, 55, 65, 67, 68, 75.

%H Pontus von Brömssen, <a href="/A394265/b394265.txt">Table of n, a(n) for n = 1..20000</a>

%H <a href="/index/Ph#Pi314">Index entries for sequences related to the number Pi</a>.

%e    |      | frequencies f_i of 0-9 in first a(n) digits |

%e  n | a(n) |         0  1  2  3  4  5  6  7  8  9        | max |f_i/a(n)-1/10|

%e ---+------+---------------------------------------------+---------------------

%e  1 |   1  |         0  0  0  1  0  0  0  0  0  0        |  9/10  = 0.9

%e  2 |   2  |         0  1  0  1  0  0  0  0  0  0        |  2/5   = 0.4

%e  3 |   3  |         0  1  0  1  1  0  0  0  0  0        |  7/30  = 0.233333...

%e  4 |   7  |         0  2  1  1  1  1  0  0  0  1        | 13/70  = 0.185714...

%e  5 |   8  |         0  2  1  1  1  1  1  0  0  1        |  3/20  = 0.15

%e  6 |   9  |         0  2  1  1  1  2  1  0  0  1        | 11/90  = 0.122222...

%e  7 |  10  |         0  2  1  2  1  2  1  0  0  1        |  1/10  = 0.1

%e  8 |  36  |         1  2  5  7  3  4  3  2  5  4        | 17/180 = 0.094444...

%e  9 |  37  |         1  2  5  7  4  4  3  2  5  4        | 33/370 = 0.089189...

%e 10 |  38  |         1  3  5  7  4  4  3  2  5  4        |  8/95  = 0.084210...

%e 11 |  39  |         1  3  5  7  4  4  3  2  5  5        | 31/390 = 0.079487...

%e 12 |  40  |         1  3  5  7  4  4  3  3  5  5        |  3/40  = 0.075

%Y Cf. A000796, A039624, A278977, A278978, A278979, A393333, A394263 (Euclidean distance), A394264 (Manhattan distance).

%K nonn,base

%O 1,2

%A _Pontus von Brömssen_, Mar 14 2026