A249272 - OEIS

%I #19 Jun 13 2021 14:12:24

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

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

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

%N Decimal expansion of a constant associated with fundamental discriminants and Dirichlet characters.

%H Peter J. Cho, Henry H. Kim, <a href="http://arxiv.org/abs/1601.03012">The average of the smallest prime in a conjugacy class</a>, arXiv:1601.03012 [math.NT], 2016.

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

%H Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 250.

%H P. Pollack, <a href="http://dx.doi.org/10.1016/j.jnt.2011.12.015">The average least quadratic nonresidue modulo m and other variations on a theme of Erdős</a>, J. Number Theory 132 (2012) 1185-1202.

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

%e 4.9809473396149341507913253258807752812377326965852...

%t digits = 103; Clear[s, P]; P[j_] := P[j] = Product[(Prime[k] + 2)/(2*(Prime[k] + 1)), {k, 1, j - 1}] // N[#, digits + 100]&; s[m_] := s[m] = Sum[Prime[j]^2/(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

%o (PARI) suminf(k=1, prime(k)^2/(2*(prime(k)+1))*prod(i=1, k-1, (prime(i)+2)/(2*(prime(i)+1)))); \\ _Michel Marcus_, Apr 15 2017

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

%K nonn,cons

%O 1,1

%A _Jean-François Alcover_, Oct 24 2014