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URL: https://oeis.org/A394265

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A394265
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.
3
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, 77, 78, 79, 94, 95, 97, 98, 99, 100, 124, 140, 479, 487, 549, 557, 560, 561, 568, 570, 576, 578, 585, 592, 623, 626, 627, 632, 634, 635, 636, 637, 638, 639, 640, 695
OFFSET
1,2
COMMENTS
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:
base 2: 1, 3, 4;
base 3: 1, 2, 6, 11, 12, 13, 14, 15;
base 4: 1, 2, 4;
base 5: 1, 2, 7, 8, 9, 22, 23, 26, 30, 43, 46, 47, 53, 54, 55, 65, 67, 68, 75.
EXAMPLE
| | frequencies f_i of 0-9 in first a(n) digits |
n | a(n) | 0 1 2 3 4 5 6 7 8 9 | max |f_i/a(n)-1/10|
---+------+---------------------------------------------+---------------------
1 | 1 | 0 0 0 1 0 0 0 0 0 0 | 9/10 = 0.9
2 | 2 | 0 1 0 1 0 0 0 0 0 0 | 2/5 = 0.4
3 | 3 | 0 1 0 1 1 0 0 0 0 0 | 7/30 = 0.233333...
4 | 7 | 0 2 1 1 1 1 0 0 0 1 | 13/70 = 0.185714...
5 | 8 | 0 2 1 1 1 1 1 0 0 1 | 3/20 = 0.15
6 | 9 | 0 2 1 1 1 2 1 0 0 1 | 11/90 = 0.122222...
7 | 10 | 0 2 1 2 1 2 1 0 0 1 | 1/10 = 0.1
8 | 36 | 1 2 5 7 3 4 3 2 5 4 | 17/180 = 0.094444...
9 | 37 | 1 2 5 7 4 4 3 2 5 4 | 33/370 = 0.089189...
10 | 38 | 1 3 5 7 4 4 3 2 5 4 | 8/95 = 0.084210...
11 | 39 | 1 3 5 7 4 4 3 2 5 5 | 31/390 = 0.079487...
12 | 40 | 1 3 5 7 4 4 3 3 5 5 | 3/40 = 0.075
CROSSREFS
Cf. A000796, A039624, A278977, A278978, A278979, A393333, A394263 (Euclidean distance), A394264 (Manhattan distance).
Sequence in context: A249587 A007607 A370902 * A076682 A327224 A386673
KEYWORD
nonn,base
AUTHOR
STATUS
approved