A167372 a(n) = A120301(A123944(n))/A058313(A123944(n)).

5, 7, 11, 5, 13, 7, 17, 7, 37, 19, 29, 119, 47, 41, 23, 5, 29, 31, 37, 11, 37, 41, 43, 13, 7, 13, 71, 13, 49, 13, 7, 47, 7, 7, 53, 79, 59, 61, 5, 97, 71, 103, 67, 71, 17, 73, 61, 139, 17, 17, 79, 19, 19, 19, 19, 83, 151, 89, 29, 97, 263, 29, 101, 103, 223, 107, 109, 271, 37, 23, 113, 359

Offset: 1

Author

Alexander Adamchuk, Nov 02 2009

Keywords

• nonn

Comments

The ratio A120301(n)/A058313(n) = 1 for most n.

a(n) is prime for most n.

The first composite ratio a(12) = 119 = 7*17 corresponds to A123944(12) = 238.

The next two composite ratios a(29) = a(76) = 49 = 7^2 correspond to A123944(29) = 1470 and A123944(76) = 10290. [Edited by Petros Hadjicostas, May 09 2020]

Crossrefs

Cf. A058313, A120301, A123944.

Programs

Mathematica

f = 0; Do[f = f + (-1)^(n + 1) * 1/n; g = Abs[(2(-1)^n * n + (-1)^n - 1)/4] * f; rfg = Numerator[g]/Numerator[f]; If[(rfg == 1) == False, Print[rfg]], {n, 1500}]

PARI

lista(nn) = {for (n=1, nn, my(sn = sum(k=1, n, (-1)^(k+1)/k)); if ((s=numerator(sn)) != (ss=abs(numerator((-1/4) * (2*(-1)^n*n + (-1)^n - 1) * sn))), print1(ss/s, ", ")););} \\ Michel Marcus, May 10 2020

Extensions

a(32)-a(46) from Petros Hadjicostas, May 09 2020, using Michel Marcus's program and the data from A123944

a(47)-a(72) from Petros Hadjicostas, May 09 2020, using the Mathematica program