A122989 Decimal expansion of Sum_{n >= 1} 1/A007504(n), where A007504(n) is the sum of the first n primes.

1, 0, 2, 3, 4, 7, 6, 3, 2, 3, 9, 2, 0, 1, 2

Offset

1,3

Comments

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

Summed through k = 2562700000000 primes. Upper bound = 1.0234763239201294. Lower bound = 1.0234763239201286. - Robert Price, May 05 2013

Links

Table of n, a(n) for n=1..15.

Example

1/2 + 1/5 + 1/10 + 1/17 + 1/28 + 1/41 + 1/58 + 1/77 + 1/100 + ... = 1.023476329...

Crossrefs

Cf. A007504.

Sequence in context: A336321 A359446 A072275 * A222246 A353828 A321726

Adjacent sequences: A122986 A122987 A122988 * A122990 A122991 A122992

Keyword

cons,nonn,more

Author

Pierre CAMI, Oct 28 2006

Extensions

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

Corrected a(10), added a(11)-a(15) from Robert Price, May 05 2013

Status

approved