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

1,2

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

Links

Table of n, a(n) for n=1..15.

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

M. Kamada, Near-repdigit-related prime numbers

Example

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

Mathematica

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

Prog

(PARI) for(n=1, 9999, if(ispseudoprime(10^n*(10^n-1)-1), print1(n", ")))
(Magma) [n: n in [0..200] | IsPrime(10^n*(10^n-1)-1)]; // Vincenzo Librandi, Dec 08 2015

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.

Sequence in context: A191011 A351734 A053490 * A375661 A375672 A367881

Adjacent sequences: A265380 A265381 A265382 * A265384 A265385 A265386

Keyword

nonn,more

Author

Serge Batalov, Dec 07 2015

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

Status

approved