

A122989


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


1



1, 0, 2, 3, 4, 7, 6, 3, 2, 3, 9, 2, 0, 1, 2
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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: A167151 A273014 A072275 * A222246 A321726 A267299
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



