A024530 Numerator of -Sum_{k=1..n} (-1)^k / prime(k).

0, 1, 1, 11, 47, 727, 7141, 151427, 2366603, 64131559, 1636722341, 57208085801, 1916138684507, 85982424199597, 3392993977055461, 172553478253276697, 8530444564835173531, 535885387802465283059, 30766248305796169627529

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• frac
• easy
• nice

Comments

Limit of the fractional values is A078437. - Charles R Greathouse IV, Apr 22 2011

Examples

			0/1, 1/2, 1/6, 11/30, 47/210, 727/2310, 7141/30030, 151427/510510, ...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..350 (terms n = 1..100 from T. D. Noe)

Crossrefs

Denominators are A002110.

Cf. A024451, A078437.

Programs

Maple

A024530 := n->numer(add((-1)^(k+1)/ithprime(k),k=1..n));

Mathematica

a[n_] := Numerator[ -Total[(-1)^Range[n] / Prime[ Range[n]]]]; Table[a[n], {n, 0, 18}] (* Jean-François Alcover, Dec 12 2011 *)

PARI

a(n)=numerator(-sum(k=1,n,(-1)^k/prime(k)));
concat(0, vector(33,n,a(n)))  /* show terms */

Formula

a(n+1) = a(n)*prime(n+1) + (-1)^n*primorial(prime(n)) for n >= 2. - Alexandre Herrera, Sep 03 2023

Extensions

a(0)=0 prepended by Seiichi Manyama, Jul 25 2021