A020449

It has been some months since I took a breather from my number obsessions. But I got intrigued by OEIS sequence A020449 and had Mathematica calculate 20240321 terms of these anti-Yarborough primes (download a zip file of the unindexed tabular data @ 58 MB).

 1 11
 2 101
 3 10111
 4 101111
 5 1011001
 6 1100101
 7 10010101
 8 10011101
 9 10100011
10 10101101
11 10110011
12 10111001
13 11000111
14 11100101
15 11110111
16 11111101
17 100100111
18 100111001
19 101001001
20 101001011
21 101100011
22 101101111
23 101111011
24 101111111
25 110010101
26 110101001
27 110111011
28 111000101
29 111001001
30 111010111
31 1000001011
32 1000010101
33 1000011011
34 1000110101
35 1001000111
   ...

The concatenation of the above first 35 terms is a 286-digit prime. The repunit primes are at indices 1 (R2), 15674 (R19), and 209496 (R23). The number of 1- to 30-digit terms is:

 1 0

 2 1

 3 1

 4 0

 5 1

 6 1

 7 2

 8 10

 9 14

10 29

11 54

12 104

13 198

14 281

15 580

16 1060

17 2134

18 3815

19 7389

20 13525

21 27422

22 51221

23 101654

24 185840

25 369628

26 678964

27 1348897

28 2562235

29 5170253

30 9715008

   ...

We end up (roughly) doubling the solution count with every additional digit. Next up I'll have a look at a subsequence: A157711.