A269300 Leading term in the sifting limit for Buchstab's iteration sieve.

2, 4, 4, 5, 1, 8, 5, 8, 6, 1, 3, 2, 4, 2, 5, 7, 4, 3, 8, 5, 1, 5, 6, 2, 8, 8, 0, 5, 7, 1, 8, 1, 0, 0, 7, 7, 8, 2, 4, 5, 7, 8, 2, 7, 6, 5, 3, 7, 5, 3, 7, 0, 8, 3, 1, 0, 9, 5, 6, 5, 8, 2, 7, 2, 0, 3, 8, 7, 0, 1, 6, 1, 6, 7, 8, 1, 4

Offset

1,1

References

George Greaves, Sieves in Number Theory (2001). See p. 4 and pp. 293-294.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

N. C. Ankeny and H. Onishi, The general sieve, Acta Arithmetica 10 (1964/1965), pp. 31-62. See theorems 2.4 and 2.5.

H. Iwaniec, J. van de Lune, and H. J. J. te Riele, The limits of Buchstab's iteration sieve, Indagationes Mathematicae 83:4 (1980), pp. 409-417.

Formula

2*exp(li(2)-gamma-1)/log(2)^2, where gamma is Euler's constant A001620.

Example

2.44518586132425743851562880571810077824578276537537083109565827203870...

Mathematica

RealDigits[2*Exp[LogIntegral[2] - EulerGamma - 1]/Log[2]^2, 10, 100][[1]] (* G. C. Greubel, Sep 07 2018 *)

Prog

(PARI) 2*exp(intnum(s=0, log(2), (exp(s)-1)/s)-log(log(2))-1)
(PARI) 2*exp(real(-eint1(-log(2)))-Euler-1)/log(2)^2

Crossrefs

Cf. A001620.

Sequence in context: A009292 A009622 A232845 * A182215 A036443 A036437

Adjacent sequences: A269297 A269298 A269299 * A269301 A269302 A269303

Keyword

nonn,cons

Author

Charles R Greathouse IV, Feb 22 2016

Status

approved