A016629 -id:A016629 - cp's OEIS frontend

A153459 Decimal expansion of log_3 (6).

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

Offset: 1

N. J. A. Sloane, Oct 30 2009

Equals the Hausdorff dimension of Pascal's triangle modulo 3 (A083093). In general, the dimension of Pascal's triangle modulo a prime p is log(p*(p+1)/2) / log(p) (see Reiter link, theorem 2 page 117). - Bernard Schott, Dec 01 2022

			1.6309297535714574370995271143427608542995856401318804278706...

Vincenzo Librandi, Table of n, a(n) for n = 1..1000.
A. M. Reiter, Determining the dimension of fractals generated by Pascal's triangle, Fibonacci Quarterly, 31(2), 1993, pp. 112-120.
Wikipedia, List of fractals by Hausdorff dimension (see Pascal triangle modulo 3).
Index entries for transcendental numbers

cf. A002391, A016629, A083093, A102525.

evalf(log(6)/log(3),80); # Bernard Schott, Dec 01 2022

RealDigits[Log[3, 6], 10, 120][[1]] (* Vincenzo Librandi, Aug 29 2013 *)

Equals A016629 / A002391 = 1 + A102525. - Bernard Schott, Dec 01 2022

A196567 Decimal expansion of log(log(6)).

Original entry on oeis.org

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

Offset: 0

Kausthub Gudipati, Oct 04 2011

			0.583198080782659297909468269363637488177....

Cf. A016629, A074785, A194562.

evalf(log(log(6))) ; # R. J. Mathar, Oct 13 2011

RealDigits[Log[Log[6]],10,120][[1]] (* Harvey P. Dale, Mar 27 2016 *)

log(log(6)) \\ Charles R Greathouse IV, May 15 2019

A335089 Decimal expansion of log(Pi^2/6).

Original entry on oeis.org

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

Offset: 0

Terry D. Grant, Sep 11 2020

			Equals 1/(2^2) + 1/(3^2) + (1/(4^2))*(1/2) + 1/(5^2) + + 1/(7^2) + (1/(8^2))*(1/3) + ... = 0.4977003024707...

Mathematics Stack Exchange, Infinite series involving Von Mangoldt's function.
Grant Sanderson, What makes the natural log "natural"?, 3Blue1Brown video (2020).
Eric Weisstein's World of Mathematics, Mangold Function.
Eric Weisstein's World of Mathematics, Prime Zeta Function.

Cf. A000796, A013661, A053510, A131659, A016629.

Cf. A100995, A014963, A025474, A246655.

RealDigits[Log[Pi^2/6], 10, 120][[1]]
RealDigits[Sum[PrimeZetaP[2 k]/k, {k, 1, inf}], 10, 120][[1]]

log(Pi^2/6) \\ Michel Marcus, Sep 15 2020

Equals Sum_{k>=2} MangoldtLambda(k) / ((k^2)*log(k)).
Equals Sum_{k>=1} (1/k)*(1/(A246655(n)^2)) where k is the exponent of the prime power, A025474(n+1).
Equals Sum_{k>=1} primezeta(2*k)/k.
Equals 2*log(Pi) - log(6).
Equals log(zeta(2)) = log(A013661).

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A153459 Decimal expansion of log_3 (6).

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A196567 Decimal expansion of log(log(6)).

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A335089 Decimal expansion of log(Pi^2/6).

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