A113209 -id:A113209 - cp's OEIS frontend

A152566 Decimal expansion of log_3(10).

2, 0, 9, 5, 9, 0, 3, 2, 7, 4, 2, 8, 9, 3, 8, 4, 6, 0, 4, 2, 9, 6, 5, 6, 7, 5, 2, 2, 0, 2, 1, 4, 0, 1, 2, 5, 0, 6, 0, 7, 5, 1, 8, 0, 0, 6, 7, 9, 7, 9, 3, 0, 1, 1, 6, 9, 2, 3, 5, 4, 5, 3, 3, 8, 6, 3, 4, 1, 7, 7, 4, 7, 7, 5, 7, 1, 9, 4, 0, 6, 2, 8, 7, 1, 6, 7, 6, 5, 8, 0, 2, 3, 0, 8, 9, 8, 1, 2, 3

Offset: 1

N. J. A. Sloane, Oct 28 2009

			2.0959032742893846042965675220214012506075180067979301169235...

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for transcendental numbers

Cf. A102524, A100831, A113209, A102525, A152565, A113210, A152566, A152549, A152564.

RealDigits[Log[3, 10], 10, 120][[1]] (* Vincenzo Librandi, Aug 29 2013 *)

log(10)/log(3) \\ Charles R Greathouse IV, Aug 06 2020

A022927 Number of integers m such that 5^n < 3^m < 5^(n+1).

Original entry on oeis.org

1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2

Offset: 0

Clark Kimberling

			From _Amiram Eldar_, Mar 01 2024: (Start)
a(0) = 1 because 5^0 = 1 < 3^1 = 3 < 5^1 = 5.
a(1) = 1 because 5^1 = 5 < 3^2 = 9 < 5^2 = 25.
a(2) = 2 because 5^2 = 25 < 3^3 = 27 < 3^4 = 81 < 5^3 = 125. (End)

Amiram Eldar, Table of n, a(n) for n = 0..10000

Cf. A022922, A113209.

Join[{1}, Differences@ Table[Floor[n * Log[3, 5]], {n, 1, 100}]] (* Amiram Eldar, Mar 01 2024 *)

Asymptotic mean: lim_{m->oo} (1/m) * Sum_{k=1..m} a(k) = log_3(5) (A113209). - Amiram Eldar, Mar 01 2024

A154542 Decimal expansion of log_3 (15).

Original entry on oeis.org

2, 4, 6, 4, 9, 7, 3, 5, 2, 0, 7, 1, 7, 9, 2, 7, 1, 6, 7, 1, 9, 7, 0, 4, 0, 4, 0, 7, 6, 7, 8, 6, 4, 0, 3, 9, 6, 3, 0, 7, 9, 3, 2, 3, 6, 6, 6, 6, 6, 0, 4, 9, 6, 8, 9, 0, 5, 2, 8, 9, 0, 3, 9, 4, 7, 9, 5, 4, 9, 2, 2, 7, 6, 1, 9, 1, 0, 2, 5, 8, 2, 3, 6, 5, 5, 5, 9, 3, 1, 1, 3, 7, 5, 9, 5, 2, 9, 4, 9

Offset: 1

N. J. A. Sloane, Oct 30 2009

			2.4649735207179271671970404076786403963079323666660496890528...

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for transcendental numbers

RealDigits[Log[3, 15], 10, 120][[1]] (* Vincenzo Librandi, Aug 29 2013 *)

Equals 1+A113209. - R. J. Mathar, Mar 21 2024

A228375 Decimal expansion of log_3(25).

Original entry on oeis.org

2, 9, 2, 9, 9, 4, 7, 0, 4, 1, 4, 3, 5, 8, 5, 4, 3, 3, 4, 3, 9, 4, 0, 8, 0, 8, 1, 5, 3, 5, 7, 2, 8, 0, 7, 9, 2, 6, 1, 5, 8, 6, 4, 7, 3, 3, 3, 3, 2, 0, 9, 9, 3, 7, 8, 1, 0, 5, 7, 8, 0, 7, 8, 9, 5, 9, 0, 9, 8, 4, 5, 5, 2, 3, 8, 2, 0, 5, 1, 6, 4, 7, 3, 1, 1, 1, 8

Offset: 1

Vincenzo Librandi, Aug 29 2013

			2.92994704143585433439408081535728079261586473333209937810578078959098...

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for transcendental numbers

Cf. decimal expansion of log_3(m): A102525 (m=2), A100831 (m=4), A113209 (m=5), A153459 (m=6), A152565 (m=7), A113210 (m=8), A152566 (m=10), A154175 (m=11), A154196 (m=12), A154217 (m=13), A154463 (m=14), A154542 (m=15), A154751 (m=16), A154848 (m=17), A152549 (m=18), A155003 (m=19), A102447 (m=20), A155541 (m=21), A155694 (m=22), A155808 (m=23), A155922 (m=24), this sequence, A152564 (m=26).

Mathematica
```
RealDigits[Log[3, 25], 10, 100][[1]]
```

Equals 2*A113209. - R. J. Mathar, Sep 08 2013

cp's OEIS Frontend

A152566 Decimal expansion of log_3(10).

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A022927 Number of integers m such that 5^n < 3^m < 5^(n+1).

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A154542 Decimal expansion of log_3 (15).

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A228375 Decimal expansion of log_3(25).

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