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.

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

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