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

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, 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, 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

Offset

1,1

Links

Table of n, a(n) for n=1..101.

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. 251.

G. Martin and P. Pollack, The average least character non-residue and further variations on a theme of Erdős, J. London Math. Soc. 87 (2013) 22-42.

Formula

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.

Example

2.1514351056861465486242810050965840532633...

Mathematica

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

Crossrefs

Cf. A232929, A232930, A232931, A232932.

Sequence in context: A289621 A069626 A348495 * A205443 A340070 A069359

Adjacent sequences: A249271 A249272 A249273 * A249275 A249276 A249277

Keyword

nonn,cons

Author

Jean-François Alcover, Oct 24 2014

Status

approved