This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A164985 #4 Jun 02 2025 01:54:03 %S A164985 1,6,27,405,1458,5103,59049,196830,649539,6908733,22320522,71744535, %T A164985 731794257,2324522934,7360989291,73222472421,230127770466, %U A164985 721764371007,7060738412025,22029503845518,68630377364883,663426981193869 %N A164985 Denominators of ternary BBP-type series for log(5). %C A164985 The formula %C A164985 log(5)=(4/27)Sum(k>=0,(1/81^k)(9/(4k+1)+3/(4k+2)+1/(4k+3))) %C A164985 can be written in unit numerators: %C A164985 log(5)=(4/3)Sum(k>=0,(1/81^k)(1/(4k+1)+1/(3*(4k+2))+1/(9*(4k+3)))), %C A164985 so the sequence of denominators inside the sum satisfies %C A164985 Sum(n>=0,1/a(n))=(3/4)log(5) %F A164985 G.f.: (1+6*x+27*x^2+243*x^3+486*x^4+729*x^5)/(1-81*x^3)^2 %o A164985 (PARI) a(n)=[(n\3*4+1),3*(n\3*4+2),9*(n\3*4+3)][n%3+1]*81^(n\3) %Y A164985 Cf. A154920. %K A164985 frac,nonn %O A164985 0,2 %A A164985 _Jaume Oliver Lafont_, Sep 03 2009