A016632 -id:A016632 - cp's OEIS frontend

A104139 Decimal expansion of log_10(9).

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

Offset: 0

Lekraj Beedassy, Mar 07 2005

			log_10(9) = 0.95424250943932487459005580651...

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for transcendental numbers

Cf. decimal expansion of log_10(m): A007524 (m = 2), A114490 (m = 3), A114493 (m = 4), A153268 (m = 5), A153496 (m = 6), A153620 (m = 7), A153790 (m = 8), this sequence, 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[N[Log[10, 9], 150]] (* Stefan Steinerberger, Mar 14 2006 *)

log(9)/log(10) \\ R. J. Mathar, Mar 11 2008

Equals A016632 / A002392 . - R. J. Mathar, Mar 11 2008

More terms from Stefan Steinerberger, Mar 14 2006

More terms from R. J. Mathar, Mar 11 2008

A154009 Decimal expansion of log_6 (9).

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Oct 30 2009

			1.2262943855309168262595077230643582470697162810857931432210...

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

Cf. decimal expansion of log_6(m): A152683 (m=2), A152935 (m=3), A153102 (m=4), A153202 (m=5), A153617 (m=7), A153754 (m=8), this sequence, A154157 (m=10), A154178 (m=11), A154199 (m=12), A154278 (m=13), A154466 (m=14), A154567 (m=15), A154776 (m=16), A154856 (m=17), A154911 (m=18), A155044 (m=19), A155490 (m=20), A155554 (m=21), A155697 (m=22), A155823 (m=23), A155959 (m=24).

SetDefaultRealField(RealField(100)); Log(9)/Log(6); // G. C. Greubel, Sep 14 2018

RealDigits[Log[6, 9], 10, 100][[1]] (* Vincenzo Librandi, Aug 31 2013 *)

default(realprecision, 100); log(9)/log(6) \\ G. C. Greubel, Sep 14 2018

Equals A016632 / A016629 =2/(1+A102525). - R. J. Mathar, Jul 29 2024

A338155 (Smallest prime >= 3^n) - (largest prime <= 3^n).

Original entry on oeis.org

0, 4, 6, 4, 10, 6, 24, 10, 6, 22, 36, 74, 30, 10, 18, 124, 44, 20, 70, 16, 60, 6, 52, 30, 34, 22, 42, 48, 144, 30, 20, 104, 122, 90, 50, 12, 52, 18, 140, 156, 72, 126, 126, 42, 68, 90, 98, 100, 66, 74, 50, 174, 30, 38, 126, 72, 30, 378, 102, 176, 108, 130

Offset: 1

A.H.M. Smeets, Oct 25 2020

nonn

Size of prime gap containing the number 3^n, for n > 1.

From Gauss's prime counting function approximation, the expected gap size should be approximately n*log(3), however, the observed values seem to be closer to n*log(8.72) ~ n*log(3^2) = n*A016632.

A.H.M. Smeets, Table of n, a(n) for n = 1..1000

Cf. A013598, A013604, A016632.

Cf. A058249 (for 2^n), A338419 (for 5^n), A338376 (for 6^n), A038804 (for 10^n).

a[1] = 0; a[n_] := First @ Differences @ NextPrime[3^n, {-1, 1}]; Array[a, 60] (* Amiram Eldar, Oct 30 2020 *)

a(n) = if (n==1, 0, nextprime(3^n) - precprime(3^n)); \\ Michel Marcus, Oct 25 2020

a(n) = A013598(n) + A013604(n) for n > 1.

A016704 Decimal expansion of log(81).

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

			4.394449154672438765580980947690102818589962231290997806938777334549977....

Harry J. Smith, Table of n, a(n) for n = 1..20000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Index entries for transcendental numbers

Cf. A016509 (continued fraction).

SetDefaultRealField(RealField(100)); Log(81); // G. C. Greubel, Sep 17 2018

RealDigits[Log[81],10,120][[1]] (* Harvey P. Dale, Feb 20 2012 *)

default(realprecision, 20080); x=log(81); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b016704.txt", n, " ", d)); \\ Harry J. Smith, May 24 2009

2 times A016632.

A016737 Continued fraction for log(9).

Original entry on oeis.org

2, 5, 14, 4, 1, 2, 2, 8, 1, 15, 1, 2, 1, 8, 2, 7, 1, 3, 3, 1, 1, 1, 2, 17, 1, 4, 2, 1, 2, 6, 1, 2, 2, 5, 1, 1, 2, 2, 1, 1, 1, 27, 3, 3, 4, 1, 1, 306, 2, 1, 1, 2, 3, 1, 1, 4, 5, 1, 1, 38, 1, 4, 1, 6, 1, 11, 10, 1, 9, 10, 2, 5, 2, 1, 3, 8, 1, 2, 3, 6, 1, 4, 2, 3

Offset: 0

N. J. A. Sloane

			2.19722457733621938279049047... = 2 + 1/(5 + 1/(14 + 1/(4 + 1/(1 + ...)))). - _Harry J. Smith_, May 16 2009

Harry J. Smith, Table of n, a(n) for n = 0..19999
G. Xiao, Contfrac

Cf. A016632 (decimal expansion).

ContinuedFraction(2*Log(3)); // G. C. Greubel, Sep 15 2018

ContinuedFraction[Log[9],120] (* Harvey P. Dale, May 21 2017 *)

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(log(9)); for (n=1, 20000, write("b016737.txt", n-1, " ", x[n])); } \\ Harry J. Smith, May 16 2009

Offset changed by Andrew Howroyd, Jul 10 2024

A387247 Decimal expansion of (2*log(3) + 7)/8.

Original entry on oeis.org

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

Offset: 1

Stefano Spezia, Aug 24 2025

			1.149653072167027422848811309230631426161872639...

W. Lai, H. Jiang, D. Zhu, and B. Zhu, Improved Approximation Algorithm and Hardness Result for Sorting Unsigned Strings by Symmetric Reversals. In: Fomin, F.V., Xiao, M. (eds) Computing and Combinatorics. COCOON 2025. Lecture Notes in Computer Science, vol 15984. Springer, Singapore (2026).
Index entries for transcendental numbers.

Cf. A002391, A016632.

Mathematica
```
RealDigits[(2Log[3]+7)/8,10,100][[1]]
```

cp's OEIS Frontend

A104139 Decimal expansion of log_10(9).

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A154009 Decimal expansion of log_6 (9).

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A338155 (Smallest prime >= 3^n) - (largest prime <= 3^n).

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A016704 Decimal expansion of log(81).

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A016737 Continued fraction for log(9).

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A387247 Decimal expansion of (2*log(3) + 7)/8.

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