A249272 Decimal expansion of a constant associated with fundamental discriminants and Dirichlet characters.

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, 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, 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

Offset

1,1

Links

Table of n, a(n) for n=1..103.

Peter J. Cho, Henry H. Kim, The average of the smallest prime in a conjugacy class, arXiv:1601.03012 [math.NT], 2016.

Steven R. Finch, Average least nonresidues, December 4, 2013. [Cached copy, with permission of the author]

Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 250.

P. Pollack, The average least quadratic nonresidue modulo m and other variations on a theme of Erdős, J. Number Theory 132 (2012) 1185-1202.

Formula

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

Example

4.9809473396149341507913253258807752812377326965852...

Mathematica

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

Prog

(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

Crossrefs

Cf. A232929, A232930, A232931, A232932.

Sequence in context: A200398 A145424 A200394 * A280630 A215617 A328229

Adjacent sequences: A249269 A249270 A249271 * A249273 A249274 A249275

Keyword

nonn,cons

Author

Jean-François Alcover, Oct 24 2014

Status

approved