A074142 Coefficients a(n) of a series connected with the odd primes.

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

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

Table of n, a(n) for n=1..53.

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

Cf. A005097, A030018.

Sequence in context: A118208 A355650 A292892 * A059084 A246117 A295688

Adjacent sequences: A074139 A074140 A074141 * A074143 A074144 A074145

Keyword

easy,sign

Author

Zak Seidov, Sep 16 2002

Status

approved