A249271 - OEIS

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).

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

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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