

A078437


Decimal expansion of sum of alternating series of reciprocals of primes.


13



2, 6, 9, 6, 0, 6, 3, 5, 1, 9, 7, 1, 6, 7
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OFFSET

0,1


COMMENTS

Verified and extended by Chris K. Caldwell and Jud McCranie.
Next two terms are most likely 4 and 5.  Robert Price, Sep 13 2011


REFERENCES

S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, pp. 9498.


LINKS

Table of n, a(n) for n=0..13.
Eric Weisstein's World of Mathematics, Prime Sums
Eric Weisstein's World of Mathematics, Prime Zeta Function
Wikipedia, Prime Zeta Function


EXAMPLE

1/2  1/3 + 1/5  1/7 + 1/11  1/13 + ... = 0.26960635197167...


MATHEMATICA

s = NSum[ p=Prime[k//Round]; (1)^k/p, {k, 1, Infinity}, WorkingPrecision > 30, NSumTerms > 5*10^7, Method > "AlternatingSigns"]; RealDigits[s, 10, 14] // First (* JeanFrançois Alcover, Sep 02 2015 *)


CROSSREFS

Cf. A242301, A242302, A242303, A242304.
Sequence in context: A021375 A190407 A057052 * A235997 A155678 A134946
Adjacent sequences: A078434 A078435 A078436 * A078438 A078439 A078440


KEYWORD

cons,hard,more,nonn


AUTHOR

G. L. Honaker, Jr., Dec 31 2002


EXTENSIONS

Values of a(11)a(14) = 7,1,6,7 from Robert Price, Sep 13 2011


STATUS

approved



