e Digits
The constant e with decimal expansion
| e=2.718281828459045235360287471352662497757... |
(OEIS A001113) can be computed to 10^9 digits of precision in 10 CPU-minutes on modern hardware.
e was computed to 1.7×10^9 digits by P. Demichel, and the first 1.25×10^9 have been verified by X. Gourdon on Nov. 21, 1999 (Plouffe). e was computed to 10^(12) decimal digits by S. Kondo on Jul. 5, 2010 (Yee).
The Earls sequence (starting position of n copies of the digit n) for e is given for n=1, 2, ... by 2, 252, 1361, 11806, 210482, 9030286, 3548262, 141850388, 1290227011, ... (OEIS A224828).
The starting positions of the first occurrence of n in the decimal expansion of e (including the initial 2 and counting it as the first digit) are 14, 3, 1, 18, 11, 12, 21, 2, ... (OEIS A088576).
Scanning the decimal expansion of e until all n-digit numbers have occurred, the last 1-, 2-, ... digit numbers appearing are 6, 12, 548, 1769, 92994, ... (OEIS A036900), which end at digits 21, 372, 8092, 102128, ... (OEIS A036904).
The digit sequence 0123456789 does not occur in the first 10^(10) digits of e, but 9876543210 does, starting at position 6001160363 (E. Weisstein, Jul. 22, 2013).
e-constant primes (i.e., e-primes) occur at 1, 3, 7, 85, 1781, 2780, 112280, 155025, ... (OEIS A64118) decimal digits.
It is not known if e is normal, but the following table giving the counts of digits in the first 10^n terms shows that the decimal digits are very uniformly distributed up to at least 10^(10).
See also
Constant Digit Scanning, Constant Primes, e, e-Prime, Earls SequenceExplore with Wolfram|Alpha
More things to try:
References
Sloane, N. J. A. Sequences A001113/M1727, A036900, A036904, A064118, A088576, and A224828 in "The On-Line Encyclopedia of Integer Sequences."Yee, A. J. "y-cruncher - A Multi-Threaded Pi-Program." http://www.numberworld.org/y-cruncher/.Referenced on Wolfram|Alpha
e DigitsCite this as:
Weisstein, Eric W. "e Digits." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/eDigits.html