A123944 Numbers k such that A120301(k) differs from A058313(k).

19, 28, 87, 99, 104, 196, 203, 210, 222, 228, 231, 238, 281, 328, 367, 499, 579, 620, 888, 967, 1036, 1147, 1204, 1352, 1372, 1403, 1419, 1430, 1470, 1481, 1498, 1503, 1666, 1693, 1907, 2211, 2359, 2440, 2499, 2521, 2556, 2678, 2948, 3407, 3467, 3504, 3537, 3892, 4046, 4079, 4108

Offset: 1

Author

Alexander Adamchuk, Nov 22 2006

Keywords

• nonn

Comments

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

The ratio A120301(a(n))/A058313(a(n)) = {5, 7, 11, 5, 13, 7, 17, 7, 37, 10, 29, 119, 47, 41, 23, 5, 29, 31, 37, 11, 37, 41, 43, 13, 7, 13, 71, 13, 49, 13, 7,...} is prime for the most a(n).

The first composite ratio A120301(a(n))/A058313(a(n)) corresponds to a(n) = a(29) = 1470 because A120301(1470)/A058313(1470) = 49 = 7^2. [Edited by Petros Hadjicostas, May 09 2020]

Crossrefs

Cf. A058313, A120301.

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[{n,rfg}]], {n,1,15000}]

PARI

isok(n) = my(sn = sum(k=1, n, (-1)^(k+1)/k)); numerator(sn) != abs(numerator((-1/4) * (2*(-1)^n*n + (-1)^n - 1)*sn));
for (n=1, 4200, if (isok(n), print1(n, ", "))); \\ Michel Marcus, May 10 2020

Extensions

a(47)-a(51) from Petros Hadjicostas, May 09 2020