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

Author

Pierre CAMI, Oct 28 2006

Keywords

• cons
• nonn
• more

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

Examples

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

Crossrefs

Cf. A007504.

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