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Glaisher-Kinkelin Constant Digits

The decimal expansion of the Glaisher-Kinkelin constant is given by

(OEIS A074962). was computed to decimal digits by E. Weisstein (Dec. 3, 2015).

The Earls sequence (starting position of copies of the digit ) for is given for , 2, ... by 7, 14, 2264, 1179, 411556, ... (OEIS A225763).

The digit sequences 0123456789 and 9876543210 do not occur in the first digits (E. Weisstein, Dec. 3, 2015).

-constant primes occur for 7, 10, 18, 64, 71, 527, 1992, 5644, 8813, 19692, ... (OEIS A118420) decimal digits.

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

Scanning the decimal expansion of until all -digit numbers have occurred, the last 1-, 2-, ... digit numbers appearing are 5, 98, 478, 9192, ... (OEIS A000000), which end at digits 22, 495, 7233, 100426, ... (OEIS A000000).

It is not known if the Glaisher-Kinkelin constant is normal in base 10, but the following table giving the counts of digits in the first terms shows normal-appearing behavior up to at least

 OEIS 10 100 0 A000000 0 11 96 999 9890 1 A000000 2 9 102 1033 9928 2 A000000 4 16 93 992 9977 3 A000000 0 8 100 1016 10055 4 A000000 1 8 99 955 10043 5 A000000 0 5 94 979 10034 6 A000000 0 12 96 988 10121 7 A000000 1 12 114 1067 9998 8 A000000 1 11 108 1031 9999 9 A000000 1 8 98 940 9955

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

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References

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

Cite this as:

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