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A249272 Decimal expansion of a constant associated with fundamental discriminants and Dirichlet characters. 0
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 (list; constant; graph; refs; listen; history; text; internal format)
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]

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 A198548

Adjacent sequences:  A249269 A249270 A249271 * A249273 A249274 A249275

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Oct 24 2014

STATUS

approved

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Last modified September 21 17:46 EDT 2019. Contains 327273 sequences. (Running on oeis4.)