A242303 Decimal expansion of C(4), where C(x) = -Sum_{k>=1} (-1)^k/prime(k)^x.

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

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(4), after ...20007, seem to converge to a(24)=0, a(25)= 5.

Links

Table of n, a(n) for n=-1..23.

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

Example

0.05137830516674828257520007...

Mathematica

next = 0; ndigits = 13; epsilon = 10^-(2 ndigits); k = 1;
While[test = 1/Prime[k + 1]^4 - 1/Prime[k]^4; -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), A242302 (x=3), A242304 (x=5).

Cf. A085964.

Sequence in context: A327965 A094136 A051996 * A214803 A225984 A074048

Adjacent sequences: A242300 A242301 A242302 * A242304 A242305 A242306

Keyword

nonn,cons,hard,more

Author

Stanislav Sykora, May 14 2014

Status

approved