1 - 2 floor(1/3 n + 2/3) + floor(1/3 n + 1/3) + floor(1/3 n) ----------------------------------------------------------------------------- The twin primes constant. 0.660161815846869573927812110014555778432623 ----------------------------------------------------------------------------- The Varga constant, also known to be the 1/(one-ninth constant). 9.2890254919208189187554494359517450610317 One-ninth constant is 0.1076539192264845766153234450909471905879765038 ----------------------------------------------------------------------------- 0.4749493799879206503325046363279829685595493732172029822833310248 6455792917488386027427564125050214441890378494262395464775250455 2099778523950882780814821592082565202912193041770281959987798787 6404342380353179170625016170252803841553681975679189489592083858 to 256 digits is also this closed expression. 2**(5/4)*sqrt(Pi)*exp(Pi/8)*GAMMA(1/4)**(-2); ----------------------------------------------------------------------------- -Zeta(1,1/2). is also equal to -Zeta(1/2)*(1/2*gamma+1/2*ln(8*Pi)+1/4*Pi). 3.922646139209151727471531446714599513730323971506505209568298485 2547208031503382848806505231041456914038034379886764996843321856 0187370796648866325531877003002927708284792679262934379740474743 4560678349258709176744625306684542186046544092107149397014020908 ----------------------------------------------------------------------------- -Zeta(-1/2) to 256 digits. 0.2078862249773545660173067253970493022262685312876725376101135571 0614729193229234048754326694073321564310997561412868956566132691 4694458311965705623294109531061640017807007041375078320755666248 7877869206615046914282912338325693716136777293836109459387888090 ----------------------------------------------------------------------------- Zeta(2) or Pi**2/6 to 10000 places.