A324800 Numerator of Sum_{k=1..n} 1/(k*(prime(k+1)-prime(k))).

1, 5, 17, 71, 379, 389, 2843, 5791, 52679, 54191, 601141, 608071, 8071243, 8148463, 8196511, 2060389, 35567153, 11912441, 227867909, 28847227, 8275057, 33289183, 768422549, 6163315597, 30969555953, 31263744353, 94216171859, 665249876813, 19372559860777, 19394741666137, 603566081213047

Offset

1,2

Comments

The series Sum_{k=1..oo} 1/(k*(prime(k+1)-prime(k))) diverges.

References

D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, 1996, Section VII.21, 1(b), p. 248.

Links

Table of n, a(n) for n=1..31.

Example

1, 5/4, 17/12, 71/48, 379/240, 389/240, 2843/1680, 5791/3360, 52679/30240, 54191/30240, 601141/332640, 608071/332640, 8071243/4324320, ...

Mathematica

Table[Numerator[Sum[1/(k*(Prime[k+1]-Prime[k])), {k, n}]], {n, 40}] (* Vincenzo Librandi, Sep 27 2019 *)

Prog

(Magma) [Numerator(&+[1/(i*(NthPrime(i+1)-NthPrime(i))): i in [1..n]]): n in [1..35]]; // Vincenzo Librandi, Sep 27 2019

Crossrefs

Cf. A324801.

Sequence in context: A149714 A149715 A149716 * A146577 A211405 A354040

Adjacent sequences: A324797 A324798 A324799 * A324801 A324802 A324803

Keyword

nonn,frac

Author

N. J. A. Sloane, Sep 11 2019

Status

approved