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A249274 Decimal expansion of a constant associated with the set of all complex primitive Dirichlet characters. 0

%I

%S 2,1,5,1,4,3,5,1,0,5,6,8,6,1,4,6,5,4,8,6,2,4,2,8,1,0,0,5,0,9,6,5,8,4,

%T 0,5,3,2,6,3,3,0,4,5,7,1,8,5,8,4,5,7,8,9,5,8,8,9,7,3,3,3,9,1,0,7,8,1,

%U 8,4,2,8,7,3,2,5,7,4,6,4,5,2,0,7,1,8,4,6,3,0,4,2,4,4,6,9,1,7,9,3,2

%N Decimal expansion of a constant associated with the set of all complex primitive Dirichlet characters.

%H Steven R. Finch, <a href="/A232927/a232927.pdf">Average least nonresidues</a>, December 4, 2013. [Cached copy, with permission of the author]

%H G. Martin and P. Pollack, <a href="http://dx.doi.org/10.1112/jlms/jds036">The average least character non-residue and further variations on a theme of Erdős</a>, J. London Math. Soc. 87 (2013) 22-42.

%F sum_{q} q^4/((q+1)^2 (q-1)) prod_{p<q} (p^2-p-1)/((p+1)^2 (p-1)), where p, q are primes.

%e 2.1514351056861465486242810050965840532633...

%t digits = 101; Clear[s, P]; P[j_] := P[j] = Product[(Prime[k]^2 - Prime[k] - 1)/((Prime[k] + 1)^2*(Prime[k] - 1)), {k, 1, j - 1}] // N[#, digits + 100]&; s[m_] := s[m] = Sum[Prime[j]^4/((Prime[j] + 1)^2*(Prime[j] - 1))*P[j], {j, 1, m}]; s[10]; s[m = 20]; While[ RealDigits[s[m]] != RealDigits[s[m/2]], Print[m, " ", N[s[m]]]; m = 2*m]; RealDigits[s[m], 10, digits] // First

%Y Cf. A232929, A232930, A232931, A232932.

%K nonn,cons

%O 1,1

%A _Jean-François Alcover_, Oct 24 2014

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Last modified September 16 08:48 EDT 2019. Contains 327091 sequences. (Running on oeis4.)