|
|
A074142
|
|
Coefficients a(n) of a series connected with the odd primes.
|
|
0
|
|
|
1, -1, -1, 0, 0, 2, 1, 0, -2, -5, 2, 3, 5, 6, -10, -12, -9, 11, 32, 11, -5, -55, -61, 29, 84, 129, 9, -188, -232, -136, 322, 567, 255, -354, -1185, -840, 585, 2038, 2318, -594, -3909, -4761, -929, 7387, 10441, 3930, -11137, -23097, -12215, 16547, 44716, 36786, -23108
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,6
|
|
COMMENTS
|
The series reciprocal to the series with coefficients in A005097 has (integer) coefficients with irregular signs and values. In contrast the series reciprocal to the series with coefficients = primes themselves has coefficients (A030018) with alternating signs and regular growth. The radius of convergence (defined from consecutive coefficients ratio) of that series is 0.686777834460.
|
|
LINKS
|
|
|
FORMULA
|
Sum(a(i)*x^(i-1), (i=1, inf))=1/(1+sum(1/2(p(i)-1)*x^(i-1), i=2, inf)) =1/(1+sum( A005097(i)*x^(i), i=1, inf))
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,sign
|
|
AUTHOR
|
_Zak Seidov_, Sep 16 2002
|
|
STATUS
|
approved
|
|
|
|