|
Search: id:A058313
|
|
|
| A058313 |
|
Numerator of the n-th alternating harmonic number, sum ((-1)^(k+1)/k, k=1..n). |
|
+0
40
|
|
| 1, 1, 5, 7, 47, 37, 319, 533, 1879, 1627, 20417, 18107, 263111, 237371, 52279, 95549, 1768477, 1632341, 33464927, 155685007, 166770367, 156188887, 3825136961, 3602044091, 19081066231, 18051406831, 57128792093, 7751493599, 236266661971
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
A Wolstenholme-like theorem: for prime p > 3, if p = 6k-1, then p divides a(4k-1), otherwise if p = 6k+1, then p divides a(4k). - T. D. Noe (noe(AT)sspectra.com), Apr 01 2004
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=1..200
Hisanori Mishima, Factorizations of many number sequences
Hisanori Mishima, Factorizations of many number sequences
Eric Weisstein's World of Mathematics, Harmonic Number
|
|
FORMULA
|
G.f. for A058313(n)/ A058312(n) : log(1+x)/(1-x) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 15 2003
|
|
EXAMPLE
|
1, 1/2, 5/6, 7/12, 47/60, 37/60, 319/420, 533/840, 1879/2520, ...
|
|
MAPLE
|
A058313 := n->numer(add((-1)^(k+1)/k, k=1..n));
|
|
PROGRAM
|
(PARI) a(n)=(-1)^n*numerator(polcoeff(log(1-x)/(x+1)+O(x^(n+1)), n))
|
|
CROSSREFS
|
Denominators are A058312. Cf. A025530.
Apart from leading term, same as A075830.
Cf. A001008 (numerator of n-th harmonic number).
Bisections are A049281 and A082687.
Sequence in context: A090520 A066219 A075830 this_sequence A120301 A119787 A025530
Adjacent sequences: A058310 A058311 A058312 this_sequence A058314 A058315 A058316
|
|
KEYWORD
|
nonn,frac,nice,easy
|
|
AUTHOR
|
njas, Dec 09 2000
|
|
|
Search completed in 0.002 seconds
|
