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A249274 Decimal expansion of a constant associated with the set of all complex primitive Dirichlet characters. 0
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 (list; constant; graph; refs; listen; history; text; internal format)
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]

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: A161686 A289621 A069626 * A205443 A069359 A318320

Adjacent sequences:  A249271 A249272 A249273 * A249275 A249276 A249277

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Oct 24 2014

STATUS

approved

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Last modified August 25 16:41 EDT 2019. Contains 326324 sequences. (Running on oeis4.)