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A269300 Leading term in the sifting limit for Buchstab's iteration sieve. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
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

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Last modified February 28 23:19 EST 2020. Contains 332353 sequences. (Running on oeis4.)