A265383 Numbers k such that 10^k * (10^k - 1) - 1 is prime.

1, 6, 9, 154, 253, 1114, 1390, 2618, 5611, 12871, 15286, 108609, 132574, 164369, 188484

Offset: 1

Author

Serge Batalov, Dec 07 2015

Keywords

• nonn
• more

Comments

The primes arising from this construction (e.g., 999998999999) are among the primes counted in A266148. In particular, it follows that A266148(a(n)) > 0. - David A. Corneth, May 19 2016

a(16) > 188484. - Ben Meekins, Sep 08 2018

Examples

			6 is in the sequence because 10^12 - 10^6 - 1 = 999998999999 is prime.
		

Links

• Brady Haran and Simon Pampena, Glitch Primes and Cyclops Numbers, Numberphile video (2015).
• M. Kamada, Near-repdigit-related prime numbers

Crossrefs

Cf. similar sequences listed in A265481.

A098845: Similar sequence in base 2.

A183187: Numbers k such that 10^(2k+1)-10^k-1 is prime, palindromic.

A266148: Number of n-digit primes in which n-1 of the digits are 9's.

Programs

Magma

[n: n in [0..200] | IsPrime(10^n*(10^n-1)-1)]; // Vincenzo Librandi, Dec 08 2015

Mathematica

Select[Range[15000], PrimeQ[10^# (10^# - 1) - 1] &] (* Vincenzo Librandi, Dec 08 2015 *)

PARI

for(n=1,9999,if(ispseudoprime(10^n*(10^n-1)-1),print1(n", ")))

Extensions

a(11) from Kazuyoshi Asao, Feb 11 2002

a(12) from Serge Batalov, Dec 25 2015

a(13) from Ben Meekins, Feb 16 2016

a(14) from Ben Meekins, Dec 17 2016

a(15) from Ben Meekins, Sep 08 2018