A125684 a(n) = numbers n such that A125683(n) is prime.

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, 140, 170, 189, 269, 307, 365, 408, 470, 475, 546, 558, 604, 751, 771, 857, 892, 896, 992, 1031, 1080, 1181, 1228, 1289, 1342, 1465, 1483, 1491, 1520, 1525, 1571, 1620

Offset

1,1

Comments

A125683(n) = Numerator[ Sum[ (-1)^(k+1) * 1/(k(k+1)), {k,1,n} ]. Corresponding primes are listed in A125685(n) = A125683[ a(n) ] = {5,11,2,79,331,479,5297,70061,69203,8960447,45083347,...}.

Links

Table of n, a(n) for n=1..56.

Example

A125683(n) begins {1,1,5,11,2,79,331,479,493,5297,2701,69071,70061,...}.
Thus a(1) = 3 because A125683(3) = 5 is prime but A125683(k) is not prime for k<3.
a(2)-a(6) = {4,5,6,7,8} because A125683(k) is prime for 3<k<9.

Mathematica

g=0; Do[g=g+(-1)^(n+1)*1/(n(n+1)); f=Numerator[g]; If[PrimeQ[f], Print[{n, f}]], {n, 1, 1342}]

Crossrefs

Cf. A125683, A125685.

Sequence in context: A039078 A073632 A066378 * A207669 A001272 A273664

Adjacent sequences: A125681 A125682 A125683 * A125685 A125686 A125687

Keyword

hard,nonn

Author

Alexander Adamchuk, Nov 30 2006

Extensions

More terms from Amiram Eldar, Feb 18 2019

Status

approved