A242302 Decimal expansion of C(3), where C(x) = -Sum_{k>=1} (-1)^k/prime(k)^x.

9, 3, 4, 6, 3, 6, 3, 1, 3, 9, 9, 6, 4, 9, 8, 8, 9, 1, 1, 2, 4

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.

Links

Table of n, a(n) for n=-1..19.

Stanislav Sykora, PARI/GP scripts for primes-related functions, see function AltSum1DivPrimePwr(x,eps), with instruction.

Example

0.0934636313996498891124...

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).

Cf. A085541.

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

Status

approved