cp's OEIS Frontend

A351794 Decimal expansion of Sum_{k>=1} AH(k)*L(k)/2^k, where AH(k) = A058313(k)/A058312(k) is the k-th alternating harmonic number and L(k) = A000032(k) is the k-th Lucas number.

%I A351794 #11 Feb 19 2022 14:00:07
%S A351794 2,8,2,1,4,7,5,3,5,8,7,6,2,6,4,9,4,6,1,7,4,6,0,5,1,4,3,5,6,8,2,5,3,0,
%T A351794 6,3,7,2,4,6,6,5,6,6,6,9,3,4,5,4,6,9,9,1,4,7,9,8,8,9,4,1,3,7,4,2,4,9,
%U A351794 8,1,3,0,8,6,1,0,4,6,4,8,0,7,0,6,2,6,7,2,9,9,5,7,8,7,1,2,6,4,8,4,1,7,9,5,4
%N A351794 Decimal expansion of Sum_{k>=1} AH(k)*L(k)/2^k, where AH(k) = A058313(k)/A058312(k) is the k-th alternating harmonic number and L(k) = A000032(k) is the k-th Lucas number.
%F A351794 Equals 3*log(5/4) + 10*log(phi)/sqrt(5), where phi is the golden ratio (A001622).
%F A351794 Equals (4/3)*log(5/4) + (5/3)*A351789.
%e A351794 2.82147535876264946174605143568253063724665666934546...
%t A351794 RealDigits[3*Log[5/4] + 10*Log[GoldenRatio]/Sqrt[5], 10, 100][[1]]
%Y A351794 Cf. A000032, A001622, A002390, A058312, A058313, A349850, A349851, A351789.
%K A351794 nonn,cons
%O A351794 1,1
%A A351794 _Amiram Eldar_, Feb 19 2022