A331863 Numbers k such that R(k) - 10^floor(k/2-1) is prime, where R(k) = (10^k-1)/9 (repunit: A002275).

8, 12, 17, 20, 24, 42, 1124, 1169, 1538, 7902

Offset

1,1

Comments

The corresponding primes are a subsequence of A065074: near-repunit primes that contain the digit 0.

In base 10, R(k) - 10^floor(k/2-1) has ceiling(k/2) digits 1, one digit 0 and again floor(k/2-1) digits 1: for even as well as odd k, there is a digit 0 just right of the middle of the repunit of length k.

No term can be congruent to 1 (mod 3). - Chai Wah Wu, Feb 07 2020

Links

Table of n, a(n) for n=1..10.

Example

For k = 8,  R(8)  - 10^(4-1) = 11110111 is prime.
For k = 12, R(12) - 10^(6-1) = 111111011111 is prime.
For k = 17, R(12) - 10^(8-1) = 11111111101111111 is prime.

Prog

(PARI) for(n=2, 9999, isprime(p=10^n\9-10^(n\2-1))&&print1(n", "))

Crossrefs

Cf. A002275 (repunits), A011557 (powers of 10), A065074 (near-repunit primes that contain the digit 0), A138148 (Cyclop numbers with digits 0 & 1).

Cf. A331862 (variant with floor(n/2) instead of floor(n/2-1)), A331860 (variant with + (digit 2) instead of - (digit 0)).

Sequence in context: A036705 A129150 A361160 * A175975 A030752 A091523

Adjacent sequences: A331860 A331861 A331862 * A331864 A331865 A331866

Keyword

nonn,hard,more,base

Author

M. F. Hasler, Jan 30 2020

Extensions

a(7)-a(10) from Giovanni Resta, Jan 31 2020

Status

approved