A249271 - OEIS

%I #9 Dec 20 2017 11:25:34

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

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

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

%N Decimal expansion of the mean value over all positive integers of a function giving the least quadratic nonresidue modulo a given odd integer (this function is precisely defined in A053761).

%D Steven R. Finch, Mathematical Constants, Cambridge Univ. Press, 2003, Meissel-Mertens constants: Quadratic residues, pp. 96—98.

%H Robert Baillie and Samuel S. Wagstaff, <a href="http://www.ams.org/journals/mcom/1980-35-152/S0025-5718-1980-0583518-6/home.html">Lucas pseudoprimes</a>, Mathematics of Computation 35 (1980), pp. 1391-1417.

%F 1 + sum_{j=2..m} (p_j + 1)*2^(-j+1)*prod_{i=1..j-1} (1 - 1/p_i), where p_j is the j-th prime number.

%e 3.147755148502400312516674955879769209272937748793398864...

%t digits = 104; Clear[s]; s[m_] := s[m] = 1 + Sum[(Prime[j] + 1)*2^(-j + 1)* Product[1 - 1/Prime[i], {i, 1, j - 1}] // N[#, digits + 100]&, {j, 2, m}] ; s[10]; s[m = 20]; While[RealDigits[s[m]] != RealDigits[s[m/2]], Print[m]; m = 2*m]; RealDigits[s[m], 10, digits] // First

%o (PARI) do(lim)=my(p=2,pr=1.,s=1); forprime(q=3,lim, pr*=(1-1/p)/2; s+=(q+1)*pr; p=q); s \\ _Charles R Greathouse IV_, Dec 20 2017

%Y Cf. A053760, A053761, A098990.

%K nonn,cons

%O 1,1

%A _Jean-François Alcover_, Oct 24 2014