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A249270 Decimal expansion of the mean value over all positive integers of the least prime not dividing a given integer. 0
2, 9, 2, 0, 0, 5, 0, 9, 7, 7, 3, 1, 6, 1, 3, 4, 7, 1, 2, 0, 9, 2, 5, 6, 2, 9, 1, 7, 1, 1, 2, 0, 1, 9, 4, 6, 8, 0, 0, 2, 7, 2, 7, 8, 9, 9, 3, 2, 1, 4, 2, 6, 7, 1, 9, 7, 7, 2, 6, 8, 2, 5, 3, 3, 1, 0, 7, 7, 3, 3, 7, 7, 2, 1, 2, 7, 7, 6, 6, 1, 2, 4, 1, 9, 0, 1, 7, 8, 1, 1, 2, 3, 1, 7, 5, 8, 3, 7, 4, 2, 2, 9, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

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

LINKS

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

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

Dylan Fridman et al., A prime-representing constant, Amer. Math. Monthly 126 (2019), 72-73 (on ResearchGate).

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

Sum_{k >= 0} 1/A034386(k). - Jani Melik, Jul 22 2015

EXAMPLE

2.9200509773161347120925629171120194680027278993214267...

MATHEMATICA

digits = 103; Clear[s]; s[m_] := s[m] = Sum[(Prime[k] - 1)/Product[Prime[j], {j, 1, k - 1}] // N[#, digits + 100]&, {k, 1, m}]; s[10]; s[m = 20]; While[RealDigits[s[m]] != RealDigits[s[m/2]], m = 2*m]; RealDigits[s[m], 10, digits] // First

PROG

(Sage)

def sharp_primorial(n): return sloane.A002110(prime_pi(n));

@CachedFunction

def spv(n):

b = 0

for i in (0..n):

    b = b + 1/sharp_primorial(i)

return b;

N(spv(300), digits=108) # Jani Melik, Jul 22 2015

CROSSREFS

Cf. A098990.

Sequence in context: A289632 A269919 A178418 * A153739 A298589 A272286

Adjacent sequences:  A249267 A249268 A249269 * A249271 A249272 A249273

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Oct 24 2014

STATUS

approved

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Last modified October 18 05:14 EDT 2019. Contains 328145 sequences. (Running on oeis4.)