A391473 a(n) is the smallest positive integer k such that k*R_n has digits with alternating parity, where R_n is the n-th repunit.

1, 11, 19, 371, 1891, 36911, 189091, 3690911, 18909091, 369090911, 1890909091, 36909090911, 189090909091

Offset

1,2

Links

Table of n, a(n) for n=1..13.

Formula

a(n) = A110305(A002275(n)).

Conjecture:

a(2*n) = (4060*10^(2*n - 4) + 21)/11, n >= 2.

a(2*n-1) = (208*10^(2*n - 4) + 1)/11, n >= 2.

Example

n |    R_n     |     k    |      k*R_n       |
1 | 1          | 1        | 1                |
2 | 11         | 11       | 121              |
3 | 111        | 19       | 2109             |
4 | 1111       | 371      | 412181           |
5 | 11111      | 1891     | 21010901         |
6 | 111111     | 36911    | 4101218121       |
7 | 1111111    | 189091   | 210101090101     |
8 | 11111111   | 3690911  | 41010121812121   |
9 | 111111111  | 18909091 | 2101010109010101 |

Crossrefs

Cf. A030141, A110304, A002275.

Subsequence of A110305.

Sequence in context: A032370 A295834 A129908 * A344431 A129909 A174976

Adjacent sequences: A391470 A391471 A391472 * A391474 A391475 A391476

Keyword

nonn,base,more

Author

Gonzalo Martínez, Dec 10 2025

Extensions

a(11)-a(13) from Michael S. Branicky, Dec 11 2025

Status

approved