Golomb-Dickman Constant Digits

The Golomb-Dickman constant digits are the decimal digits of the Golomb-Dickman constant, whose decimal expansion begins

(OEIS A084945). Mitchell (1968) computed to 53 decimal places. has been computed to decimal digits by E. Weisstein (Jul. 25, 2013). Positions below count from 1 at the first decimal digit after the decimal point.

The Earls sequence records the starting position of the first occurrence of the string formed by concatenation of copies of the decimal representation of the positive integer . For and , 2, ..., it begins 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 decimal strings of length have occurred, including those with leading zeros, the last strings for , 2, ... are 1, 33, 821, ..., which end at positions 28, 587, 6322, ....

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 in base 10. The following table gives reported counts of each decimal digit in the first decimal digits after the decimal point.

	OEIS	10	100
0		0	9	89	987
1		0	7	108	999
2		2	12	93	996
3		1	10	94	989
4		1	9	100	1021
5		1	12	98	983
6		1	10	104	1042
7		0	5	96	995
8		2	14	109	993
9		2	12	109	995

The first few -constant primes are 624329, 624329988543550870992936383, ... (OEIS A174975), which have integer lengths 6, 27, 57, 60, 1659, 2508, ... (OEIS A174974). E. W. Weisstein reported a completed search for primes through decimal digits (Jul. 25, 2013). The following table summarizes the largest values reported in that search.