A152566 -id:A152566 - cp's OEIS frontend

A114490 Decimal expansion of log_10(3).

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

Offset: 0

Eric W. Weisstein, Dec 01 2005

			0.477121254...

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Motzkin Number
Index entries for transcendental numbers

Cf. A114473.

Cf. decimal expansion of log_10(m): A007524 (m=2), this sequence, A114493 (m=4), A153268 (m=5), A153496 (m=6), A153620 (m=7), A153790 (m=8), A104139 (m=9), A154182 (m=11), A154203 (m=12), A154368 (m=13), A154478 (m=14), A154580 (m=15), A154794 (m=16), A154860 (m=17), A154953 (m=18), A155062 (m=19), A155522 (m=20), A155677 (m=21), A155746 (m=22), A155830 (m=23), A155979 (m=24).

RealDigits[Log[10, 3], 10, 100][[1]] (* Vincenzo Librandi, Sep 10 2013 *)

log(3)/log(10) \\ Michel Marcus, Jan 25 2015

Equals 1/A152566. - R. J. Mathar, Jul 31 2025

A054965 Beatty sequence for log_3(10), i.e., for 1/log_10(3); so largest exponent of 3 which produces an n-digit decimal number.

Original entry on oeis.org

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 132, 134, 136

Offset: 1

Henry Bottomley, Dec 13 2002

			log_10(3) = 0.477121... so a(11) = floor(11/0.477121...) = floor(23.0549...) = 23; 3^23 = 94143178827 is the largest 11 decimal digit power of 3.

Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Beatty Sequence.
Index entries for sequences related to Beatty sequences.

Cf. A062153, A066343, A074118, A152566.

Floor[Range[100]*Log[3, 10]] (* Paolo Xausa, Jul 11 2024 *)

a(n) = n*log(10)\log(3); \\ Michel Marcus, Aug 03 2017

a(n) = floor(n/log_10(3)) = log_3(A074118(n)) = A062153(A074118(n)).

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

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A114490 Decimal expansion of log_10(3).

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A054965 Beatty sequence for log_3(10), i.e., for 1/log_10(3); so largest exponent of 3 which produces an n-digit decimal number.

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A228375 Decimal expansion of log_3(25).

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