A323458 - OEIS

%I #22 May 30 2021 04:45:37

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

%T 7,3,4,6,6,4,1,5,1,3,7,7,5,7,2,0,9,9,9,3,3,2,9,3,4,2,3,9,2,1,0,4,0,4,

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

%N Decimal expansion of log(2^(1/2)*3^(1/3) / 6^(1/6)).

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F From _Jianing Song_, Jan 23 2019: (Start)

%F Equals (1/6)*log(12) = (1/6)*A016635.

%F Equals (1/3)*log(2) + (1/6)*log(3) = (1/3)*A002162 + (1/6)*A002391. (End)

%F Equals Sum_{k>=1} H(2*k-1)/4^k, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number. - _Amiram Eldar_, May 30 2021

%e 0.4141511082980000517049515799731464734664151377572...

%t RealDigits[Log[2^(1/2)*3^(1/3) / 6^(1/6)], 10, 101][[1]] (* _Georg Fischer_, Apr 04 2020 *)

%o (PARI) log( 2^(1/2)*3^(1/3) / 6^(1/6) ) \\ _Charles R Greathouse IV_, May 15 2019

%Y Suggested by A230191.

%Y Cf. A002162, A002391, A016635.

%Y Cf. A001008, A002805.

%K nonn,cons

%O 0,1

%A _N. J. A. Sloane_, Jan 20 2019

%E a(99) corrected by _Georg Fischer_, Apr 04 2020