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A123944
Numbers n such that A120301(n) differs from A058313(n).
1
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]
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
Sequence in context: A120144 A255924 A067452 * A095046 A166667 A121458
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Nov 22 2006
EXTENSIONS
a(47)-a(51) from Petros Hadjicostas, May 09 2020
STATUS
approved