A020773 -id:A020773 - cp's OEIS frontend

A069181 Decimal expansion of 1/1024.

0, 0, 0, 9, 7, 6, 5, 6, 2, 5, 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: 0

Rick L. Shepherd, Apr 10 2002

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

Cf. A021516 (1/512), A021260 (1/256), A021132 (1/128), A021068 (1/64), A021036 (1/32), A021020 (1/16), A020821 (1/8), A020773 (1/4), A020761 (1/2).

Join[{0,0,0},RealDigits[1/1024,10,120][[1]]] (* or *) PadRight[ {0,0,0,9,7,6,5,6,2,5},120,{0}] (* Harvey P. Dale, Jan 26 2019 *)

A021108 Decimal expansion of 1/104.

Original entry on oeis.org

0, 0, 9, 6, 1, 5, 3, 8, 4, 6, 1, 5, 3, 8, 4, 6, 1, 5, 3, 8, 4, 6, 1, 5, 3, 8, 4, 6, 1, 5, 3, 8, 4, 6, 1, 5, 3, 8, 4, 6, 1, 5, 3, 8, 4, 6, 1, 5, 3, 8, 4, 6, 1, 5, 3, 8, 4, 6, 1, 5, 3, 8, 4, 6, 1, 5, 3, 8, 4, 6, 1, 5, 3, 8, 4, 6, 1, 5, 3, 8, 4, 6, 1, 5, 3, 8, 4, 6, 1, 5, 3, 8, 4, 6, 1, 5, 3, 8, 4

Offset: 0

N. J. A. Sloane

After 9, periodic with period 6: [6, 1, 5, 3, 8, 4]. See also A021030 (1/26), A021069 (1/65), A021420 (1/416), A021654 (1/650). - Bruno Berselli, Apr 13 2018

			0.009615384615384615384615384615384615384615384615384615384615384...

Index entries for linear recurrences with constant coefficients, signature (1,0,-1,1).

Join[{0, 0}, RealDigits[1/104, 10, 120][[1]]] (* or *) PadRight[{0, 0, 9, 6}, 120,{3, 8, 4, 6, 1, 5}] (* Harvey P. Dale, Aug 18 2012 *)

Equals A020821 * A021017 = A020773 * A021030 = A020761 * A021056. - Bruno Berselli, Apr 13 2018

A257936 Decimal expansion of 11/18.

Original entry on oeis.org

6, 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, 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

Offset: 0

Bruno Berselli, May 13 2015

Decimal expansion of Sum_{i>=1} 1/A028552(i).

Also, continued fraction expansion of 5+A001622.

			.6111111111111111111111111111111111111111111111111111111111111111...

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

Cf. A028552, A030880.

Cf. A010716 (decimal expansion of 5/9 = 10/18), A010722 (decimal expansion of 2/3 = 12/18).

Magma
```
[6,1^^90];
```
Mathematica
```
RealDigits[11/18, 10, 90][[1]]
```

11/18. \\ Charles R Greathouse IV, Apr 18 2016

Equals A020773 + A142464.
From Elmo R. Oliveira, Aug 05 2024: (Start)
G.f.: (6-5*x)/(1-x).
E.g.f.: exp(x) + 5.
a(n) = 1, n >= 1. (End)

A273918 Numerator of z(n), where z(n) = z(n - 1)^2 + 1/4 and z(0) = 1.

Original entry on oeis.org

1, 5, 29, 905, 835409, 698981939105, 488580362881004355588929, 238710771078004490460834598457103704776369419905

Offset: 0

Alonso del Arte, Jun 04 2016

a(8) is approximately 5.698 * 10^93.
The denominator of z(n) is 2^(2^n) for n > 0.
Given that the iteration of z(n) escapes to infinity, this shows that 1 is not in the Julia set for the function z^2 + 1/4. This is of course also true of -1.

			1^2 + 1/4 = 5/4, hence a(1) = 5.
(5/4)^2 + 1/4 = 25/16 + 4/16 = 29/16, hence a(2) = 29.

Cf. A015701, A020773.

Mathematica
```
Numerator[NestList[#^2 + 1/4 &, 1, 8]]
```

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A069181 Decimal expansion of 1/1024.

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A021108 Decimal expansion of 1/104.

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A257936 Decimal expansion of 11/18.

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A273918 Numerator of z(n), where z(n) = z(n - 1)^2 + 1/4 and z(0) = 1.

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