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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 (list; constant; graph; refs; listen; history; text; internal format)
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. 94-98.

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 (* Jean-Fran├žois 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

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Last modified August 19 19:25 EDT 2017. Contains 290821 sequences.