A309738 Primes of the form b^2*10^(2*k) + b*10^k + 1 for 1 <= b <= 9, k >= 0.

3, 7, 13, 31, 43, 73, 421, 2551, 6481, 8191, 250501, 4002001, 64008001, 81009001, 40000200001, 90000300001, 64000008000001, 400000000020000000001, 3600000000060000000001, 64000000000008000000000001, 90000000000000300000000000001, 250000000000000500000000000001

Offset

1,1

Links

Table of n, a(n) for n=1..22.

Example

b | Primes of the form b^2*10^(2*k) + b*10^k + 1
--+-------------------------------------------------------------
1 | 3.
2 | 7, 421, 4002001, 40000200001, 400000000020000000001, ...
3 | 13, 90000300001, 90000000000000300000000000001, ...
4 |
5 | 31, 2551, 250501, 250000000000000500000000000001, ...
6 | 43, 3600000000060000000001, ...
7 |
8 | 73, 6481, 64008001, 64000008000001, ...
9 | 8191, 81009001, 810000000000000000900000000000000001, ...

Crossrefs

Numbers k such that b^2*10^(2*k) + b*10^k + 1 are prime: A297422 (b=2), A306751 (b=3), A308449 (b=5), A309582 (b=6), A309719 (b=8), A309744 (b=9).

Cf. A309739.

Sequence in context: A342150 A002383 A163418 * A161218 A351318 A068679

Adjacent sequences: A309735 A309736 A309737 * A309739 A309740 A309741

Keyword

nonn,base

Author

Seiichi Manyama, Aug 15 2019

Status

approved