A123944 - OEIS

%I #25 May 10 2020 11:52:09

%S 19,28,87,99,104,196,203,210,222,228,231,238,281,328,367,499,579,620,

%T 888,967,1036,1147,1204,1352,1372,1403,1419,1430,1470,1481,1498,1503,

%U 1666,1693,1907,2211,2359,2440,2499,2521,2556,2678,2948,3407,3467,3504,3537,3892,4046,4079,4108

%N Numbers n such that A120301(n) differs from A058313(n).

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

%C 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).

%C 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]

%t 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}]

%o (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));

%o for (n=1, 4200, if (isok(n), print1(n, ", "))); \\ _Michel Marcus_, May 10 2020

%Y Cf. A058313, A120301.

%K nonn

%O 1,1

%A _Alexander Adamchuk_, Nov 22 2006

%E a(47)-a(51) from _Petros Hadjicostas_, May 09 2020