Visitar URL original
Glaisher-Kinkelin Constant Digits -- from Wolfram MathWorld
TOPICS
Search

Glaisher-Kinkelin Constant Digits


The decimal digits of the Glaisher-Kinkelin constant begin

 A=1.28242712...

(OEIS A074962). A was computed to 5×10^5 decimal digits by E. Weisstein (Dec. 3, 2015).

The Earls sequence for A gives the starting position of the first string formed by n copies of the decimal representation of n, counting from 1 after the decimal point. Its first terms, for n=1, 2, ..., are 7, 14, 2264, 1179, 411556, ... (OEIS A225763).

A scan reported no occurrence of the strings 0123456789 and 9876543210 in the first 5×10^5 decimal digits (E. Weisstein, Dec. 3, 2015).

The lengths of A-constant primes, formed by concatenation of initial decimal digits of A including the integer part, begin 7, 10, 18, 64, 71, 527, 1992, 5644, 8813, 19692, ... (OEIS A118420).

The starting positions of the first occurrence of n=0, 1, 2, ... in the decimal expansion of A (including the initial 1 and counting it as the first decimal digit) are 12, 1, 2, 18, 5, 22, 14, 7, 3, 10, ... (OEIS A229193).

Scanning the decimal expansion of A until all strings of n decimal digits have occurred, including those with leading zeros, the last 1-, 2-, ... digit strings appearing are 5, 98, 478, 9192, ..., which end at digits 22, 495, 7233, 100426, ..., counting the initial 1 as the first decimal digit.

It is not known if the Glaisher-Kinkelin constant is normal in base 10. The following table gives reported counts of each decimal digit in the first 10^n fractional decimal digits for n=1, 2, ..., 5.

d\10^nOEIS1010010^310^410^5
0011969999890
12910210339928
2416939929977
308100101610055
4189995510043
5059497910034
60129698810121
711211410679998
811110810319999
918989409955

See also

Constant Digit Scanning, Constant Primes, Glaisher-Kinkelin Constant, Glaisher-Kinkelin Constant Continued Fraction

Explore with Wolfram|Alpha

References

Sloane, N. J. A. Sequences A074962, A118420, A225763, and A229193 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Glaisher-Kinkelin Constant Digits

Cite this as:

Weisstein, Eric W. "Glaisher-Kinkelin Constant Digits." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Glaisher-KinkelinConstantDigits.html

Subject classifications