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A243350 Decimal expansion of the unique solution of the equation sum_(p prime)(1/p^x) = 1, a constant related to the asymptotic evaluation of the number of prime multiplicative compositions. 4
1, 3, 9, 9, 4, 3, 3, 3, 2, 8, 7, 2, 6, 3, 3, 0, 3, 1, 8, 2, 0, 2, 8, 0, 7, 2, 1, 4, 7, 4, 5, 6, 4, 4, 3, 2, 7, 9, 0, 4, 7, 2, 7, 4, 2, 9, 4, 8, 4, 3, 8, 3, 9, 4, 1, 2, 7, 4, 7, 6, 5, 8, 2, 2, 8, 8, 8, 0, 6, 2, 4, 9, 2, 4, 8, 7, 2, 4, 7, 8, 0, 0, 2, 3, 3, 3, 9, 0, 5, 2, 0, 0, 2, 1, 6, 6, 8, 5, 1, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.5 Kalmar's composition constant, p. 293.

LINKS

Jean-Francois Alcover, Table of n, a(n) for n = 1..100

Hugh L. Montgomery and Gérald Tenenbaum, On multiplicative compositions of integers, Mathematika 63:3 (2017), pp. 1081-1090.

Eric Weisstein's MathWorld, Prime Zeta function

EXAMPLE

1.3994333287263303182028072147456443279...

MATHEMATICA

digits = 100; eta = x /. FindRoot[PrimeZetaP[x] == 1, {x, 3/2}, WorkingPrecision -> digits+5]; RealDigits[eta, 10, digits] // First

PROG

(PARI) eps(x=1.)=my(p=if(x, precision(x), default(realprecision))); precision(2.>>(32*ceil(p*38539962/371253907))*abs(x), 9)

primezeta(s)=my(t=s*log(2), iter=lambertw(t/eps())\t, tot); forsquarefree(k=1, iter, tot+=moebius(k)/k[1]*log(abs(zeta(k[1]*s)))); tot;

solve(x=1.399, 1.4, primezeta(x)-1) \\ Charles R Greathouse IV, Nov 16 2018

(PARI) solve(x=1.05, 1.5, 1-sumeulerrat(1/p, x)) \\ Hugo Pfoertner, Nov 28 2021

CROSSREFS

Cf. A243584.

Sequence in context: A159811 A279134 A083352 * A091559 A268107 A306963

Adjacent sequences:  A243347 A243348 A243349 * A243351 A243352 A243353

KEYWORD

nonn,cons,changed

AUTHOR

Jean-François Alcover, Jun 06 2014

STATUS

approved

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Last modified December 5 10:11 EST 2021. Contains 349543 sequences. (Running on oeis4.)