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.

REFERENCES:

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