A225336 -id:A225336 - cp's OEIS frontend

A084945 Decimal expansion of Golomb-Dickman constant.

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

Offset: 0

Eric W. Weisstein, Jun 13 2003

The first 27 digits form a prime. - Jonathan Vos Post, Nov 12 2004
The first 1659 digits form a prime. - David Broadhurst, Apr 02 2010
The average number of digits in the largest prime factor of a random x-digit number is asymptotically x times this constant. - Charles R Greathouse IV, Jul 28 2015
Named after the American mathematician Solomon W. Golomb (1932 - 2016) and the Swedish actuary Karl Dickman (1861 - 1947). - Amiram Eldar, Aug 25 2020

			0.62432998854355087...

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, pp. 284-287.

David Broadhurst, PrimeForm message on the first 1659 digits, Apr 02 2010.
David Broadhurst, Titanic Golomb-Dickman prime, digest of 5 messages in primeform Yahoo group, Apr 2 - Apr 9, 2010. [Cached copy]
Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 171.
Solomon W. Golomb, Research Problem 11: Random permutations, Bull. Amer. Math. Soc. 70 (1964), p. 747.
Jeffrey C. Lagarias, Euler's constant: Euler's work and modern developments, Bull. Amer. Math. Soc., Vol. 50, No. 4 (2013), pp. 527-628, preprint, arXiv:1303.1856 [math.NT], 2013.
Andrew MacFie and Daniel Panario, Random Mappings with Restricted Preimages, in Progress in Cryptology-LATINCRYPT 2012, LNCS 7533, pp. 254-270, 2012. - From _N. J. A. Sloane_, Dec 25 2012
Simon Plouffe, The Golomb constant.
Eric Weisstein's World of Mathematics, Golomb-Dickman Constant.
Wikipedia, Golomb-Dickman constant.

Cf. A174974, A174975, A225336.

E1:= z-> int(exp(-t)/t, t=z..infinity):
lambda:= int(exp(-x-E1(x)), x=0..infinity):
s:= convert(evalf(lambda, 130), string):
seq(parse(s[n+1]), n=1..120); # Alois P. Heinz, Nov 20 2011

NIntegrate[Exp[LogIntegral[x]], {x, 0, 1}, WorkingPrecision->110, MaxRecursion->20]

intnum(x=0,1-1e-9,exp(-eint1(-log(x)))) \\ Charles R Greathouse IV, Jul 28 2015

default(realprecision, 103);
limitnum(n->intnum(x=0, 1-1/n, exp(-eint1(-log(x))))) \\ Gheorghe Coserea, Sep 26 2018

From Amiram Eldar, Aug 25 2020: (Start)
Equals Integral_{x=0..1} exp(li(x)) dx, where li(x) is the logarithmic integral.
Equals Integral_{x=0..oo} exp(-x + Ei(-x)) dx, where Ei(x) is the exponential integral.
Equals Integral_{x=0..1} F(x/(1-x)) dx, where F(x) is the Dickman function. (End)

A225364 Position of first occurrence of n in the continued fraction for the Golomb-Dickman constant.

Original entry on oeis.org

1, 8, 9, 30, 25, 18, 110, 242, 59, 100, 12, 71, 28, 153, 225, 114, 159, 66, 75, 102, 924, 6, 631, 150, 299, 434, 701, 24, 1687, 196, 1482, 779, 1552, 2658, 505, 496, 255, 46, 1626, 183, 2551, 1083, 39, 665, 1419, 678, 1676, 50, 1027, 2047, 3726, 1309, 2327

Offset: 1

Eric W. Weisstein, Jul 25 2013

			The c.f. for lambda is [0; 1, 1, 1, 1, 1, 22, 1, 2, 3, 1, ..], so
a(1) = 1 (1 occurs first at term a_1).
a(2) = 8 (2 occurs first at term a_8).
a(3) = 9 (3 occurs first at term a_9).

Eric W. Weisstein, Table of n, a(n) for n = 1..71
Eric Weisstein's World of Mathematics, Golomb-Dickman Constant Continued Fraction

Cf. A225336 (continued fraction of the Golomb-Dickman constant).

Cf. A084945 (decimal expansion of the Golomb-Dickman constant).

cp's OEIS Frontend

A084945 Decimal expansion of Golomb-Dickman constant.

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A225337 Incrementally largest terms in the continued fraction of the Golomb-Dickman constant.

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A225363 Positions of incrementally largest terms in the continued fraction expansion of the Golomb-Dickman constant.

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A225364 Position of first occurrence of n in the continued fraction for the Golomb-Dickman constant.

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