 TOPICS  # Golomb-Dickman Constant Digits

The decimal expansion of the Golomb-Dickman constant is given by (OEIS A084945). Mitchell (1968) computed to 53 decimal places. has been computed to decimal digits by E. Weisstein (Jul. 25, 2013).

The Earls sequence (starting position of copies of the digit ) for is given for , 2, ... by 28, 256, 1967, 387, ... (OEIS A225242). -constant primes occur for 6, 27, 57, 60, 1659, 2508, ... (OEIS A174974) decimal digits.

The starting positions of the first occurrence of , 1, 2, ... in the decimal expansion of (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 until all -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 digits (E. Weisstein, Jul. 25, 2013).

It is not known if is normal, but the following table giving the counts of digits in the first terms shows that the decimal digits are very uniformly distributed up to at least . OEIS 10 100  0 A000000 0 9 89 987 1 A000000 0 7 108 999 2 A000000 2 12 93 996 3 A000000 1 10 94 989 4 A000000 1 9 100 1021 5 A000000 1 12 98 983 6 A000000 1 10 104 1042 7 A000000 0 5 96 995 8 A000000 2 14 109 993 9 A000000 2 12 109 99

The first few -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 by E. W. Weisstein (Jul. 25, 2013), and the following table summarizes the largest known values.

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

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

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## References

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. https://mathworld.wolfram.com/Golomb-DickmanConstantDigits.html