A033420 -id:A033420 - cp's OEIS frontend

A052038 First nonzero digit in expansion of 1/n.

1, 5, 3, 2, 2, 1, 1, 1, 1, 1, 9, 8, 7, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9

Offset: 1

Patrick De Geest, Dec 15 1999

The number of times each digit occurs for numbers < 10^k:
...\a(n)==1.........2.......3........4........5........6........7........8........9
10^k\
1.........5.........2........1........0........1........0........0........0........0
2........55........19........9........5........5........2........2........1........1
3.......555.......186.......92.......55.......39.......26.......19.......15.......12
4......5555......1853......925......555......373......264......197......154......123
5.....55555.....18520.....9258.....5555.....3707.....2645.....1982.....1543.....1234
6....555556....185187....92591....55555....37041....26454....19839....15432....12345
7...5555555...1851854...925924...555555...370375...264549...198410...154321...123456
8..55555555..18518521..9259257..5555555..3703709..2645501..1984124..1543210..1234567
9.555555555.185185188.92592590.55555555.37037043.26455025.19841266.15432099.12345678
...
Inf. ...5/9......5/27.....5/54.....5/90.....1/27........?........?........?........?

Cf. A052039, A033330, A033420, A061861.

f[n_] := RealDigits[1/n, 10, 12][[1, 1]]; Array[f, 105]

a(n) = floor(10^floor(1+log_10(n-1))/n). After 10^k terms the number of times m will have appeared will be about 10^(k+1)/(9*m*(m+1)), e.g., 1 will appear just over 55.5% of the time. - Henry Bottomley, May 11 2001

a(n) = A000030(floor(A011557(k)/n)) for k >= A004218(n). - Reinhard Zumkeller, Feb 27 2011

A278105 a(n) = floor(3/n).

Original entry on oeis.org

3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Jason Kimberley, Nov 23 2016

Index entries for linear recurrences with constant coefficients, signature (1).

Cf. A033322, A033324, ..., A033420, A033421, A033422, A033427, A033426, A033425, A033424, A033423.

This sequence is (ignoring the trailing zeros) the third row of A010766.

Magma
```
[3 div n: n in[1..100]];
```

Table[Floor[3/n], {n, 105}] (* Michael De Vlieger, Nov 24 2016 *)

a(n) = A033322(n)+A154272(n). - R. J. Mathar, Jun 21 2025

A061861 First two significant digits of 1/n written in decimal.

Original entry on oeis.org

10, 50, 33, 25, 20, 16, 14, 12, 11, 10, 90, 83, 76, 71, 66, 62, 58, 55, 52, 50, 47, 45, 43, 41, 40, 38, 37, 35, 34, 33, 32, 31, 30, 29, 28, 27, 27, 26, 25, 25, 24, 23, 23, 22, 22, 21, 21, 20, 20, 20, 19, 19, 18, 18, 18, 17, 17, 17, 16, 16, 16, 16, 15, 15, 15, 15, 14, 14, 14

Offset: 1

Henry Bottomley, May 11 2001

After 10^k terms the number of times m will have appeared will be about 10^(k+2)/(9*m*(m+1)); e.g., 10 will appear just over 10.1% of the time.

			a(32)=31 since 1/32 = 0.0312500000...

Cf. A033420, A033421, A052038.

Table[FromDigits[RealDigits[1/n,10,2][[1]]],{n,70}] (* Harvey P. Dale, Jan 19 2018 *)

a(n) = floor(10^floor(2+log_10(n-1))/n).

cp's OEIS Frontend

A052038 First nonzero digit in expansion of 1/n.

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A278105 a(n) = floor(3/n).

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A061861 First two significant digits of 1/n written in decimal.

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