



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
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OFFSET

1,1


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]


LINKS

Table of n, a(n) for n=1..72.


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}]


PROG

(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


CROSSREFS

Cf. A058313, A120301, A123944.
Sequence in context: A119653 A023592 A076546 * A023590 A096919 A023594
Adjacent sequences: A167369 A167370 A167371 * A167373 A167374 A167375


KEYWORD

nonn


AUTHOR

Alexander Adamchuk, Nov 02 2009


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


STATUS

approved



