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# Catalan's Constant Digits

Based on methods developer in collaboration with M. Leclert, Catalan (1865) computed the constant

(OEIS A006752) now known as Catalans' constant to 9 decimals. In 1867, M. Bresse subsequently computed to 24 decimal places using a technique from Kummer. Glaisher evaluated to 20 (Glaisher 1877) and subsequently 32 decimal digits (Glaisher 1913). Catalan's constant was computed to decimal digits by A. Roberts on Dec. 13, 2010 (Yee).

The Earls sequence (starting position of copies of the digit ) for Catalan's constant is given for , 2, ... by 2, 107, 1225, 596, 32187, 185043, 20444527, 92589355, 3487283621, ... (OEIS A224819).

-constant primes occur for 52, 276, 25477, ... (OEIS A118328) digits.

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 A224615 0 6 98 976 9828 99620 999784 9998686 99996067 1 A224616 2 18 94 1039 9832 99697 1000293 10003813 100006305 2 A224696 0 10 93 980 10078 100168 1001789 10005122 100000806 3 A224706 0 7 104 1014 9859 99580 999672 9995676 100001483 4 A224717 1 11 107 961 10051 100074 1000165 9995377 100001871 5 A224774 3 10 89 1003 10062 100053 999965 9999309 100000777 6 A224775 1 12 78 985 9986 100201 998712 10000674 99998816 7 A224816 0 11 124 1032 10028 100083 1000510 10003863 100000576 8 A224817 0 3 102 1058 10192 100352 999298 9997437 100000863 9 A224818 3 12 111 952 10084 100172 999812 10000043 99992436

The digits 0123456789 do not occur in the first decimal digits of , but 9876543210 does (once), starting at position 2748123761 (E. Weisstein, Aug. 7, 2013).

Catalan's Constant, Catalan's Constant Continued Fraction, Constant Digit Scanning, Constant Primes, Earls Sequence

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## References

Glaisher, J. W. L. "On a Numerical Continued Product." Messenger Math. 6, 71-76, 1877.Glaisher, J. W. L. "Numerical Values of the Series for , 4, 6." Messenger Math. 42, 35-58, 1913.Sloane, N. J. A. Sequences A118328 and A224819 in "The On-Line Encyclopedia of Integer Sequences."Yee, A. J. "y-cruncher - A Multi-Threaded Pi-Program." http://www.numberworld.org/y-cruncher/.

## Cite this as:

Weisstein, Eric W. "Catalan's Constant Digits." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CatalansConstantDigits.html