A125685 Primes in A125683(n) = numerator[ Sum[ (-1)^(k+1) * 1/(k(k+1)), {k,1,n} ].

5, 11, 2, 79, 331, 479, 5297, 70061, 69203, 8960447, 45083347, 1031626241, 15484789693, 15537907043, 64166447971, 3979714828967, 3988907823167, 27918983997629, 598858179567591121853, 31710728461561839214229

Offset

1,1

Comments

Corresponding numbers n such that A125683(n) is prime are listed in A125684(n) = {3,4,5,6,7,8,10,13,14,18,21,22,26,27,28,32,33,35,51,54,58,67,76,89,100,...}.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..65

Formula

a(n) = A125683[ A125684(n) ].

Example

A125683(n) begins {1,1,5,11,2,79,331,479,493,5297,2701,69071,70061,...}.
Thus a(1) = 5 because A125683(3) = 5 is prime but A125683(k) is not prime for k<3.
a(2)-a(6) = {11,2,79,331,479} because A125683(k) is prime for 3<k<9.

Mathematica

 Select[Table[Numerator[Sum[(-1)^(k+1)*1/(k(k+1)), {k, 1, n}]], {n, 1, 100}], PrimeQ]

Crossrefs

Cf. A125683, A125684.

Sequence in context: A111118 A159199 A125683 * A098147 A100298 A066461

Adjacent sequences: A125682 A125683 A125684 * A125686 A125687 A125688

Keyword

nonn

Author

Alexander Adamchuk, Nov 30 2006

Status

approved