A094999 -id:A094999 - cp's OEIS frontend

A094969 a(n) = floor(5^n/2^n).

1, 2, 6, 15, 39, 97, 244, 610, 1525, 3814, 9536, 23841, 59604, 149011, 372529, 931322, 2328306, 5820766, 14551915, 36379788, 90949470, 227373675, 568434188, 1421085471, 3552713678, 8881784197, 22204460492, 55511151231, 138777878078, 346944695195, 867361737988

Offset: 0

Robert G. Wilson v, May 26 2004

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Cf. A002379, A094970-A094999.

[Floor(5^n / 2^n): n in [0..30]]; // Vincenzo Librandi, Sep 08 2011

A094969:=n->floor(5^n/2^n): seq(A094969(n), n=0..40); # Wesley Ivan Hurt, Feb 22 2017

Table[ Floor[(5/2)^n], {n, 0, 30}]
Floor[(5/2)^Range[0,30]] (* Harvey P. Dale, Jul 16 2012 *)

A094969(n):=floor(5^n/2^n)$ makelist(A094969(n),n,0,30); /* Martin Ettl, Oct 25 2012 */

a(n)=5^n>>n \\ Charles R Greathouse IV, Sep 08 2011

A094500 Least number k such that (n+1)^k / n^k >= 2.

Original entry on oeis.org

1, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10, 11, 11, 12, 13, 13, 14, 15, 15, 16, 17, 17, 18, 19, 20, 20, 21, 22, 22, 23, 24, 24, 25, 26, 26, 27, 28, 29, 29, 30, 31, 31, 32, 33, 33, 34, 35, 36, 36, 37, 38, 38, 39, 40, 40, 41, 42, 42, 43, 44, 45, 45, 46, 47, 47, 48, 49, 49, 50, 51, 51

Offset: 1

Robert G. Wilson v, May 26 2004

This sequence also describes the minimum number of (n+1)-player games, where each player has an equal chance of winning, that must be played for a given player to have at least a 50% chance of winning at least once. E.g., a(3) = 3 because in a 4-player random game, a given player will have a greater than 50% chance of winning at least once if 3 games are played. - Bryan Jacobs (bryanjj(AT)gmail.com), Apr 28 2006
Also, a(n) denotes a median m of the geometric random variable on the positive integers with mean value n+1. The median is obtained by solving 1-(n/n+1)^m >= 1/2 for least integer m. - Dennis P. Walsh, Aug 13 2012
The limit n -> inf. a(n)/n = log 2. - Robert G. Wilson v, May 13 2014

			a(3) = 3 because (4/3)^2 < 2 and (4/3)^3 > 2.

Jon Eivind Vatne, The sequence of middle divisors is unbounded, Journal of Number Theory, Volume 172, March 2017, Pages 413-415. See n(i) p. 414.

Cf. A002379, A094969-A094999.

f[n_] := Block[{k = 1}, While[((n + 1)/n)^k < 2, k++]; k]; Array[f, 75]
(* to view the limit *) Array[ f/# &, 1000] (* Robert G. Wilson v, May 13 2014 *)

a(n)=ceil(log(2)/log(1+1/n)) \\ Charles R Greathouse IV, Sep 02 2015

a(n) = n*log(2) + O(1). - Charles R Greathouse IV, Sep 02 2015

Edited by Jon E. Schoenfield, Apr 26 2014

A094970 a(n) = floor(7^n/2^n).

Original entry on oeis.org

1, 3, 12, 42, 150, 525, 1838, 6433, 22518, 78815, 275854, 965491, 3379220, 11827271, 41395451, 144884079, 507094277, 1774829971, 6211904899, 21741667147, 76095835015, 266335422555, 932173978944, 3262608926305, 11419131242070, 39966959347247, 139884357715364, 489595252003776

Offset: 0

Robert G. Wilson v, May 26 2004

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Cf. A002379, A094969-A094999.

[Floor(7^n / 2^n): n in [0..30]]; // Vincenzo Librandi, Sep 08 2011

Mathematica
```
Table[ Floor[(7/2)^n], {n, 0, 30}]
```

A094970(n):=floor(7^n/2^n)$ makelist(A094970(n),n,0,30); /* Martin Ettl, Oct 25 2012 */

a(n)=7^n>>n \\ Charles R Greathouse IV, Feb 04 2016

7^n = a(n)*2^n + A138616(n). - R. J. Mathar, Oct 26 2012

A094976 a(n) = floor(8^n/3^n).

Original entry on oeis.org

1, 2, 7, 18, 50, 134, 359, 958, 2557, 6818, 18183, 48490, 129307, 344820, 919522, 2452059, 6538825, 17436866, 46498311, 123995496, 330654658, 881745755, 2351322014, 6270192038, 16720512102, 44588032273, 118901419396

Offset: 0

Robert G. Wilson v, May 26 2004

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Cf. A002379, A094969-A094999.

[Floor(8^n / 3^n): n in [0..40]]; // Vincenzo Librandi, Sep 08 2011

Mathematica
```
Table[ Floor[(8/3)^n], {n, 0, 30}]
```

a(n) = 8^n\3^n; \\ Michel Marcus, Oct 05 2017

A094997 a(n) = floor(11^n/9^n).

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 3, 4, 4, 6, 7, 9, 11, 13, 16, 20, 24, 30, 37, 45, 55, 67, 82, 101, 123, 150, 184, 225, 275, 336, 411, 503, 614, 751, 918, 1122, 1372, 1677, 2049, 2505, 3062, 3742, 4574, 5590, 6832, 8351, 10207, 12475, 15247, 18636, 22777, 27839, 34025, 41587

Offset: 0

Robert G. Wilson v, May 26 2004

Vincenzo Librandi, Table of n, a(n) for n = 0..900

Cf. A002379, A094969-A094999.

[Floor(11^n / 9^n): n in [0..70]]; // Vincenzo Librandi, Sep 09 2011

Mathematica
```
Table[ Floor[(11/9)^n], {n, 0, 30}]
```

A094971 a(n) = floor(9^n/2^n).

Original entry on oeis.org

1, 4, 20, 91, 410, 1845, 8303, 37366, 168151, 756680, 3405062, 15322783, 68952523, 310286355, 1396288601, 6283298708, 28274844190, 127236798856, 572565594852, 2576545176835, 11594453295761, 52175039830928, 234787679239180

Offset: 0

Robert G. Wilson v, May 26 2004

Vincenzo Librandi, Table of n, a(n) for n = 0..900

Cf. A002379, A094969-A094999.

[Floor(9^n / 2^n): n in [0..30]]; // Vincenzo Librandi, Sep 08 2011

Mathematica
```
Table[ Floor[(9/2)^n], {n, 0, 30}]
```

a(n)=9^n>>n \\ Charles R Greathouse IV, Feb 04 2016

A094972 a(n) = floor(11^n/2^n).

Original entry on oeis.org

1, 5, 30, 166, 915, 5032, 27680, 152243, 837339, 4605366, 25329516, 139312339, 766217865, 4214198259, 23178090428, 127479497357, 701137235467, 3856254795069, 21209401372879, 116651707550839, 641584391529617

Offset: 0

Robert G. Wilson v, May 26 2004

Vincenzo Librandi, Table of n, a(n) for n = 0..900

Cf. A000079, A001020.

Cf. A002379, A094969-A094999.

[Floor(11^n / 2^n): n in [0..30]]; // Vincenzo Librandi, Sep 08 2011

Mathematica
```
Table[ Floor[(11/2)^n], {n, 0, 30}]
```

A094972(n):=floor(11^n/2^n)$ makelist(A094972(n),n,0,60); /* Martin Ettl, Oct 25 2012 */

a(n)=11^n>>n \\ Charles R Greathouse IV, Feb 04 2016

A094974 a(n) = floor(5^n/3^n).

Original entry on oeis.org

1, 1, 2, 4, 7, 12, 21, 35, 59, 99, 165, 275, 459, 765, 1276, 2126, 3544, 5907, 9846, 16410, 27351, 45585, 75975, 126625, 211042, 351737, 586229, 977048, 1628414, 2714024, 4523373, 7538956, 12564927, 20941545, 34902576, 58170960, 96951601

Offset: 0

Robert G. Wilson v, May 26 2004

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Cf. A002379, A094969-A094999.

[Floor(5^n / 3^n): n in [0..40]]; // Vincenzo Librandi, Sep 08 2011

Mathematica
```
Table[ Floor[(5/3)^n], {n, 0, 30}]
```

A094975 a(n) = floor(7^n/3^n).

Original entry on oeis.org

1, 2, 5, 12, 29, 69, 161, 376, 878, 2050, 4783, 11162, 26044, 60771, 141799, 330865, 772020, 1801380, 4203220, 9807513, 22884198, 53396463, 124591747, 290714077, 678332846, 1582776641, 3693145496, 8617339492, 20107125483, 46916626127

Offset: 0

Robert G. Wilson v, May 26 2004

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Cf. A000244, A000420.

Cf. A002379, A094969 - A094999.

[Floor(7^n / 3^n): n in [0..40]]; // Vincenzo Librandi, Sep 08 2011

Mathematica
```
Table[ Floor[(7/3)^n], {n, 0, 30}]
```

A094975(n):=floor(7^n/3^n)$ makelist(A094975(n),n,0,60); /* Martin Ettl, Oct 25 2012 */

a(n)=7^n\3^n \\ Charles R Greathouse IV, Sep 08 2011

A094977 a(n) = floor(10^n/3^n).

Original entry on oeis.org

1, 3, 11, 37, 123, 411, 1371, 4572, 15241, 50805, 169350, 564502, 1881676, 6272254, 20907515, 69691719, 232305731, 774352437, 2581174791, 8603915972, 28679719907, 95599066359, 318663554532, 1062211848441, 3540706161472

Offset: 0

Robert G. Wilson v, May 26 2004

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Cf. A002379, A094969-A094999.

[Floor(10^n / 3^n): n in [0..30]]; // Vincenzo Librandi, Sep 08 2011

Mathematica
```
Table[ Floor[(10/3)^n], {n, 0, 30}]
```

cp's OEIS Frontend

A094969 a(n) = floor(5^n/2^n).

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A094500 Least number k such that (n+1)^k / n^k >= 2.

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A094970 a(n) = floor(7^n/2^n).

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A094976 a(n) = floor(8^n/3^n).

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A094997 a(n) = floor(11^n/9^n).

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Magma

Mathematica

A094971 a(n) = floor(9^n/2^n).

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Magma

Mathematica

PARI

A094972 a(n) = floor(11^n/2^n).

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Author

Keywords

Links

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Programs

Magma

Mathematica

Maxima

PARI

A094974 a(n) = floor(5^n/3^n).

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