|
Search: id:A086239
|
|
|
| A086239 |
|
Decimal expansion of sum(c[k]/prime[k], k=2..infinity), where c[k]=-1 if p==1 (mod 4) and c[k]=+1 if p==3 (mod 4). |
|
+0
3
|
|
| 3, 3, 4, 9, 8, 1, 3, 2, 5, 2, 9, 9, 9, 9, 3, 1, 8, 1, 0, 6, 3, 3, 1, 7, 1, 2, 1, 4, 8, 7, 5, 4, 3, 5, 7, 3, 7, 7, 9, 9, 7, 5, 3, 8, 0, 7, 5, 5, 0, 7, 7, 0, 4, 8, 1, 0, 8, 0, 2, 0, 5, 7, 8, 8, 4, 5, 2, 2, 2, 8, 4, 3, 2, 7, 1, 8, 8, 4, 1, 1, 0, 6, 2, 4, 8, 9, 9, 6, 3, 1, 0, 2, 9, 8, 0, 3, 3, 4, 5, 3, 9, 2, 4, 8, 6
(list; cons; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
This is sum_{p prime, p>=3} -(-4/p)/p where (-4/.) is the Legendre symbol and is equal to - L(1,(-4/.)) plus an absolutely convergent sum (and therefore converges).
|
|
REFERENCES
|
Henri Cohen, "High Precision Computation of Hardy-Littlewood Constants", preprint (1991), http://www.math.u-bordeaux.fr/~cohen/hardylw.dvi [From M. F. Hasler (MHasler(AT)univ-ag.fr), Oct 29 2009]
S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, pp. 94-98
|
|
LINKS
|
D. Broadhurst, post in primenumbers group, Oct 29 2009 [From M. F. Hasler (MHasler(AT)univ-ag.fr), Oct 29 2009]
Eric Weisstein's World of Mathematics, PrimeSums
|
|
EXAMPLE
|
0.33498132529999...
|
|
PROGRAM
|
(PARI) /* the given number of primes and terms in the sum yield over 105 correct digits */ { P=vector(15, k, (2-prime(k)%4)/prime(k)); -sum(s=1, 60, moebius(s)/s*log( prod( k=2, #P, 1-P[k]^s, if(s%2, if(s==1, Pi/4, sumalt(k=0, (-1)^k/(2*k+1)^s)) , zeta(s)*(1-1/2^s) ))), sum(k=2, #P, P[k], .))} \\ [From M. F. Hasler (MHasler(AT)univ-ag.fr), Oct 29 2009]
|
|
CROSSREFS
|
Sequence in context: A019466 A111573 A049854 this_sequence A016605 A060372 A128036
Adjacent sequences: A086236 A086237 A086238 this_sequence A086240 A086241 A086242
|
|
KEYWORD
|
nonn,cons
|
|
AUTHOR
|
Eric Weisstein (eric(AT)weisstein.com), Jul 13, 2003
|
|
EXTENSIONS
|
Edited by N. J. A. Sloane (njas(AT)research.att.com), Jun 10 2008
Corrected a(9) and example, added a(10)-a(104) following Broadhurst and Cohen. - M. F. Hasler, Oct 29 2009
|
|
|
Search completed in 0.002 seconds
|
