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

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

1,1

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]

Links

Table of n, a(n) for n=1..51.

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}]

Prog

(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

Crossrefs

Cf. A058313, A120301.

Sequence in context: A120144 A255924 A067452 * A095046 A166667 A121458

Adjacent sequences: A123941 A123942 A123943 * A123945 A123946 A123947

Keyword

nonn

Author

Alexander Adamchuk, Nov 22 2006

Extensions

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

Status

approved