

A242302


Decimal expansion of C(3), where C(x) = Sum_{k>=1} (1)^k/prime(k)^x.


6



9, 3, 4, 6, 3, 6, 3, 1, 3, 9, 9, 6, 4, 9, 8, 8, 9, 1, 1, 2, 4, 9, 0, 3, 3, 1, 3, 9, 2, 4, 6, 5, 5, 7
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OFFSET

1,1


COMMENTS

The alternating series of reciprocal powers of prime numbers converges for any x > 0 (absolutely so if x > 1) but is hard to compute.
The next digits of C(3), after ...91124, seem to converge to a(20)=9, a(21)=0.
After ...9033139246557, the next digit, a(33), seems likely to be 7 or 8.  Jon E. Schoenfield, Dec 28 2017


LINKS

Table of n, a(n) for n=1..32.
S. Sykora, PARI/GP scripts for primesrelated functions, see function AltSum1DivPrimePwr(x,eps), with instruction


EXAMPLE

0.09346363139964988911249033139246557...


MATHEMATICA

next = 0; ndigits = 11; epsilon = 10^(2 ndigits); k = 1;
While[test = 1/Prime[k + 1]^3  1/Prime[k]^3; test > epsilon,
next = next + test; k += 2];
First[RealDigits[next, 10, ndigits]] (* Robert Price, Sep 07 2019 *)


PROG

(PARI) See Sykora link.


CROSSREFS

Cf. A078437 (x=1), A242301 (x=2), A242303 (x=4), A242304 (x=5).
Sequence in context: A273017 A222233 A021111 * A102754 A225455 A154184
Adjacent sequences: A242299 A242300 A242301 * A242303 A242304 A242305


KEYWORD

nonn,cons,hard,more


AUTHOR

Stanislav Sykora, May 14 2014


EXTENSIONS

a(20)a(32) from Jon E. Schoenfield, Dec 28 2017


STATUS

approved



