a(13)-a(22) for A279860
Here is the definition of A279860 from OEIS:
a(n) is the first n-digit substring to repeat in the decimal expansion of e.
There is ongoing competition[1, 2] to find such repeated sequences in π, A197123, so I took a crack at the second-most-famous transcendental constant.
I searched the first 250 billion digits and found a(1)
-a(22)
.
a(23)
was not found (I only had a 26.8% chance of finding it).
I used a HashSet but would probably switch to a bloom filter for a(24)
or higher.
Rather than partitioning by prefix, I used the least significant bits of the sequence as a hash and used modulo partitioning.
Here are the sequences and their positions:
n | a(n) | First Position | Repeat Position |
---|---|---|---|
1 | 2 | 0 | 4 |
2 | 18 | 2 | 6 |
3 | 182 | 2 | 6 |
4 | 1828 | 2 | 6 |
5 | 98793 | 478 | 494 |
6 | 987931 | 478 | 494 |
7 | 4349076 | 170 | 2731 |
8 | 82549802 | 11449 | 23544 |
9 | 450388721 | 9832 | 29424 |
10 | 5291493974 | 35210 | 159929 |
11 | 72883660263 | 55704 | 172254 |
12 | 476539957100 | 685615 | 947487 |
13 | 2557556217677 | 696773 | 4212711 |
14 | 45820090256930 | 937385 | 11527854 |
15 | 441340408673681 | 16824283 | 64070443 |
16 | 4413404086736815 | 16824283 | 64070443 |
17 | 04490816865108378 | 305179147 | 305519388 |
18 | 044908168651083787 | 305179147 | 305519388 |
19 | 3369635849169468729 | 3493534312 | 4849639160 |
20 | 29845348176416445308 | 15006890876 | 15441233099 |
21 | 561387588857094780748 | 33340537999 | 55184810049 |
22 | 8238609087161769234440 | 161691630698 | 176191766517 |