cp's OEIS Frontend

A303658 Decimal expansion of the alternating sum of the reciprocals of the triangular numbers.

%I A303658 #29 May 24 2025 10:34:08
%S A303658 7,7,2,5,8,8,7,2,2,2,3,9,7,8,1,2,3,7,6,6,8,9,2,8,4,8,5,8,3,2,7,0,6,2,
%T A303658 7,2,3,0,2,0,0,0,5,3,7,4,4,1,0,2,1,0,1,6,4,8,2,7,2,0,0,3,7,9,7,3,5,7,
%U A303658 4,4,8,7,8,7,8,7,7,8,8,6,2,4,2,3,4,5,3
%N A303658 Decimal expansion of the alternating sum of the reciprocals of the triangular numbers.
%F A303658 Equals log(16/e^2) = log(16) - 2.
%F A303658 Equals Sum_{k>=0} 1/((k+2)*2^k) = Sum_{k>=2} 1/A057711(k). - _Amiram Eldar_, Aug 19 2020
%F A303658 Equals 1 - Sum_{k>=1} 1/(k*(k+1)*(2*k+1)). - _Davide Rotondo_, May 24 2025
%e A303658 1/1 - 1/3 + 1/6 - 1/10 + 1/15 - 1/21 + ... = 0.77258872223978123766892848583270627230200053744102...
%t A303658 RealDigits[4*Log[2] - 2, 10, 100][[1]] (* _Amiram Eldar_, Aug 19 2020 *)
%t A303658 RealDigits[Log[16]-2,10,120][[1]] (* _Harvey P. Dale_, Apr 30 2022 *)
%o A303658 (PARI) sumalt(n=1, (-1)^(n+1)*2/(n*(n+1))) \\ _Michel Marcus_, Apr 28 2018
%o A303658 (PARI) log(16)-2 \\ _Altug Alkan_, May 07 2018
%Y A303658 Cf. A000217 (triangular numbers), A057711.
%Y A303658 Apart from leading digit the same as A016639 (log(16)).
%K A303658 nonn,cons
%O A303658 0,1
%A A303658 _Jon E. Schoenfield_, Apr 28 2018