|
%I #16 Jan 27 2019 18:04:10
%S 1,0,2,3,4,7,6,3,2,3,9,2,0,1,2
%N Decimal expansion of Sum_{n >= 1} 1/A007504(n), where A007504(n) is the sum of the first n primes.
%C Summing k=4016708412 primes, I get prime(k)=97434417233, primeSum=191462469311735988657, seriesSum=1.02347632390000000000618+. And I compute an upper bound of 1.02347632395-. - _Don Reble_, May 14 2007
%C Summed through k = 2562700000000 primes. Upper bound = 1.0234763239201294. Lower bound = 1.0234763239201286. - _Robert Price_, May 05 2013
%e 1/2 + 1/5 + 1/10 + 1/17 + 1/28 + 1/41 + 1/58 + 1/77 + 1/100 + ... = 1.023476329...
%Y Cf. A007504.
%K cons,nonn,more
%O 1,3
%A _Pierre CAMI_, Oct 28 2006
%E A number of contributors worked on the difficult question of computing this constant accurately. The above comment from _Don Reble_ gives the tightest bounds presently known. It had been suggested that the true value might be Pi/6 + 1/2 = 1.0235987755982988730771..., but that is now disproved. - _N. J. A. Sloane_, Jun 15 2007
%E Corrected a(10), added a(11)-a(15) from _Robert Price_, May 05 2013
|
