A249273 Decimal expansion of a constant associated with the set of all complex nonprincipal Dirichlet characters.

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

Offset

1,1

Links

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

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

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_{k >= 1} p_k^2/((p_1 + 1)(p_2 + 1)...(p_k + 1)), where p_k is the k-th prime number.

Example

2.5350541803604388301655300071859083508611780138537...

Mathematica

digits = 103; Clear[s]; s[m_] := s[m] = Sum[Prime[k]^2/Product[Prime[j] + 1, {j, 1, k}] , {k, 1, m}] // N[#, digits + 100]&; 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: A261645 A193724 A266407 * A078376 A226123 A368658

Adjacent sequences: A249270 A249271 A249272 * A249274 A249275 A249276

Keyword

nonn,cons

Author

Jean-François Alcover, Oct 24 2014

Status

approved