# sum of 1/A007504(n)

T. D. Noe noe at sspectra.com
Mon May 14 20:14:04 CEST 2007

```Using primes up to 1e6 I get

%48 = 1.023474393262367314520463960

below the PARI/gp code.

M.H.

A122989()={ local( preci=10, sp=0, s=0.);
forprime(p=1,1000000, sp+=p; s+=1/sp;
if(sp>preci, print("Using primes up to p=",p," we get s=",s);preci*=10);
);s}

(15:34) gp > A122989()                preci*=10););s
Using primes up to p=7 we get s=0.8588235294117647058823529412
Using primes up to p=29 we get s=0.9669083893103433831885127907
Using primes up to p=97 we get s=1.005057326714068069917068590
Using primes up to p=337 we get s=1.018013585652788074430261988
Using primes up to p=1153 we get s=1.021867662517188793356496650
Using primes up to p=3943 we get s=1.023000611541789149569364917
Using primes up to p=13441 we get s=1.023335007523311052968510288
Using primes up to p=45197 we get s=1.023434079911788726379668415
Using primes up to p=151091 we get s=1.023463626282318065002491187
Using primes up to p=502259 we get s=1.023472489376872091186799820
%48 = 1.023474393262367314520463960

On 5/14/07, N. J. A. Sloane <njas at research.att.com> wrote:
>
> Dear Seqfans,  A correspondent,
> "fabio mercurio" <mercurio.fabio at gmail.com>
> writes to say that this number
>
> %I A122989
> %S A122989 1,0,2,3,4,7,6,3,2
> %N A122989 Decimal expansion of Sum_{n >= 1} 1/A007504(n), where A007504(n) is the sum of the f\
> irst n primes.
> %e A122989 1/2+1/5+1/10+1/17+1/28+1/41+1/58+1/77+1/100+... = 1.02347632...
> %Y A122989 Cf. A007504.
> %Y A122989 Adjacent sequences: A122986 A122987 A122988 this_sequence A122990 A122991 A122992
> %Y A122989 Sequence in context: A026237 A125150 A072275 this_sequence A077223 A055265 A117922
> %K A122989 cons,nonn,more
> %O A122989 1,3
> %A A122989 Pierre CAMI (pierrecami(AT)tele2.fr), Oct 28 2006
>
> is really equal to 1/2 + Pi/6.  But the agreement is
> not very close.  Can someone compute more decimal places?
>
> Thanks
>
> Neil
>

```