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A249271 Decimal expansion of the mean value over all positive integers of a function giving the least quadratic nonresidue modulo a given odd integer (this function is precisely defined in A053761). 0
3, 1, 4, 7, 7, 5, 5, 1, 4, 8, 5, 0, 2, 4, 0, 0, 3, 1, 2, 5, 1, 6, 6, 7, 4, 9, 5, 5, 8, 7, 9, 7, 6, 9, 2, 0, 9, 2, 7, 2, 9, 3, 7, 7, 4, 8, 7, 9, 3, 3, 9, 8, 8, 6, 4, 0, 5, 9, 6, 4, 7, 0, 2, 0, 6, 6, 4, 7, 8, 1, 1, 8, 0, 0, 9, 1, 6, 7, 2, 4, 6, 7, 7, 9, 9, 7, 9, 4, 5, 2, 0, 9, 4, 8, 8, 2, 8, 7, 9, 7, 8, 6, 9, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge Univ. Press, 2003, Meissel-Mertens constants: Quadratic residues, pp. 96—98.

LINKS

Table of n, a(n) for n=1..104.

Robert Baillie and Samuel S. Wagstaff, Lucas pseudoprimes, Mathematics of Computation 35 (1980), pp. 1391-1417.

FORMULA

1 + sum_{j=2..m} (p_j + 1)*2^(-j+1)*prod_{i=1..j-1} (1 - 1/p_i), where p_j is the j-th prime number.

EXAMPLE

3.147755148502400312516674955879769209272937748793398864...

MATHEMATICA

digits = 104; Clear[s]; s[m_] := s[m] = 1 + Sum[(Prime[j] + 1)*2^(-j + 1)* Product[1 - 1/Prime[i], {i, 1, j - 1}] // N[#, digits + 100]&, {j, 2, m}] ; s[10]; s[m = 20]; While[RealDigits[s[m]] != RealDigits[s[m/2]], Print[m]; m = 2*m]; RealDigits[s[m], 10, digits] // First

PROG

(PARI) do(lim)=my(p=2, pr=1., s=1); forprime(q=3, lim, pr*=(1-1/p)/2; s+=(q+1)*pr; p=q); s \\ Charles R Greathouse IV, Dec 20 2017

CROSSREFS

Cf. A053760, A053761, A098990.

Sequence in context: A209418 A193969 A169838 * A272439 A217151 A081255

Adjacent sequences:  A249268 A249269 A249270 * A249272 A249273 A249274

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Oct 24 2014

STATUS

approved

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Last modified September 19 04:52 EDT 2019. Contains 327187 sequences. (Running on oeis4.)