A275689 - OEIS

%I #16 May 27 2023 04:18:07

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

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

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

%N Decimal expansion of 3*zeta(3)/(4*log(2)).

%C As it appears that the Sum {n>=1} (-1)^(n+1)/n^2 / Sum {n>=1} ((-1)^(n+1))/n^1 is the inverse of Levy's constant, or more traditionally the log of Levy's constant (A100199), this sequence which is equal to Sum {n>=1} (-1)^(n+1)/n^3 / Sum {n>=1} ((-1)^(n+1))/n^1 may be the inverse of the log of another constant with similar properties.

%F 3*zeta(3)/4*log(2) = A197070 / A002162 = Sum {n>=1} (-1)^(n+1)/n^3 / Sum {n>=1} ((-1)^(n+1))/n^1

%e 1.300651149791018703323...

%t RealDigits[3*Zeta[3]/(4*Log[2]), 10, 120][[1]] (* _Amiram Eldar_, May 27 2023 *)

%o (PARI) 3*zeta(3)/log(16) \\ _Charles R Greathouse IV_, Aug 05 2016

%o (PARI) sumalt(n=1,(-1)^n/n^3)/sumalt(n=1,(-1)^n/n) \\ _Charles R Greathouse IV_, Aug 05 2016

%Y Cf. A197070, A002162, A100199.

%K nonn,cons

%O 1,2

%A _Terry D. Grant_, Aug 05 2016