Golomb-Dickman Constant Digits

The decimal expansion of the Golomb-Dickman constant is given by


(OEIS A084945). Mitchell (1968) computed lambda to 53 decimal places. lambda has been computed to 15000 decimal digits by E. Weisstein (Jul. 25, 2013).

The Earls sequence (starting position of n copies of the digit n) for lambda is given for n=1, 2, ... by 28, 256, 1967, 387, ... (OEIS A225242).

lambda-constant primes occur for 6, 27, 57, 60, 1659, 2508, ... (OEIS A174974) decimal digits.

The starting positions of the first occurrence of n=0, 1, 2, ... in the decimal expansion of lambda (not including the initial 0 to the left of the decimal point) are 15, 28, 2, 4, 3, 10, 1, 17, 8, 6, ... (OEIS A229195).

Scanning the decimal expansion of lambda until all n-digit numbers have occurred, the last 1-, 2-, ... digit numbers appearing are 1, 33, 821, ... (OEIS A000000), which end at digits 28, 587, 6322, ... (OEIS A000000).

The digit sequences 0123456789 and 9876543210 do not occur in the first 15000 digits (E. Weisstein, Jul. 25, 2013).

It is not known if lambda is normal, but the following table giving the counts of digits in the first 10^n terms shows that the decimal digits are very uniformly distributed up to at least 10^4.


The first few lambda-constant primes are 624329, 624329988543550870992936383, ... (OEIS A174975), which have integer lengths 6, 27, 57, 60, 1659, 2508, ... (OEIS A174974). The search for primes has been completed up to 15000 by E. W. Weisstein (Jul. 25, 2013), and the following table summarizes the largest known values.

decimal digitsdiscoverer
1659D. J. Broadhurst (Apr. 2, 2010)
2508E. W. Weisstein (Apr. 3, 2010)

See also

Constant Digit Scanning, Constant Primes, Golomb-Dickman Constant, Golomb-Dickman Constant Continued Fraction

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Sloane, N. J. A. Sequences A084945, A174974, A225242, and A229195 in "The On-Line Encyclopedia of Integer Sequences."

Cite this as:

Weisstein, Eric W. "Golomb-Dickman Constant Digits." From MathWorld--A Wolfram Web Resource.

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