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A074142
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Coefficients a(n) of a series connected with the odd primes.
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0
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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; internal format)
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OFFSET
| 1,6
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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.
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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))
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CROSSREFS
| Cf. A005097, A030018.
Sequence in context: A146162 A147702 A118208 * A059084 A070677 A029584
Adjacent sequences: A074139 A074140 A074141 * A074143 A074144 A074145
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KEYWORD
| easy,sign
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AUTHOR
| Zak Seidov (zakseidov(AT)yahoo.com), Sep 16 2002
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