A331860 Numbers k such that R(k) + 10^floor(k/2-1) is prime, where R(k) = (10^k-1)/9 (repunit: A002275).

6, 7, 12, 31, 58, 127, 454, 556, 558, 604, 2944, 8118, 12078, 16942, 26268, 45198

Offset: 1

Author

M. F. Hasler, Jan 30 2020

Keywords

• nonn
• base
• hard
• more

Comments

The corresponding primes are near-repunit primes, cf. A105992.

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

No term can be congruent to 2 (mod 3). - Chai Wah Wu, Feb 07 2020

Examples

			For n = 6,  R(6)  + 10^(3-1) = 111211 is prime.
For n = 7,  R(7)  + 10^(3-1) = 1111211 is prime.
For n = 12, R(12) + 10^(6-1) = 111111211111 is prime.
		

Links

• Brady Haran and Simon Pampena, Glitch Primes and Cyclops Numbers, Numberphile video (2015).

Crossrefs

Cf. A105992 (near-repunit primes), A002275 (repunits), A011557 (powers of 10).

Cf. A331861 (variant with floor(n/2) instead of floor(n/2-1)), A331863 (variant with - (digit 0) instead of + (digit 2)).

Programs

PARI

for(n=2,999,isprime(p=10^n\9+10^(n\2-1))&&print1(n","))

Extensions

a(8)-a(14) from Giovanni Resta, Jan 31 2020

a(15)-a(16) from Michael S. Branicky, Jul 23 2024