A265383 - OEIS

%I #96 May 03 2024 23:22:54

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

%T 188484

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

%C 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

%C a(16) > 188484. - _Ben Meekins_, Sep 08 2018

%H Brady Haran and Simon Pampena, <a href="https://www.youtube.com/watch?v=HPfAnX5blO0">Glitch Primes and Cyclops Numbers</a>, Numberphile video (2015).

%H M. Kamada, <a href="https://stdkmd.net/nrr/prime/">Near-repdigit-related prime numbers</a>

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

%t Select[Range[15000], PrimeQ[10^# (10^# - 1) - 1] &] (* _Vincenzo Librandi_, Dec 08 2015 *)

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

%o (Magma) [n: n in [0..200] | IsPrime(10^n*(10^n-1)-1)]; // _Vincenzo Librandi_, Dec 08 2015

%Y Cf. similar sequences listed in A265481.

%Y A098845: Similar sequence in base 2.

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

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

%K nonn,more

%O 1,2

%A _Serge Batalov_, Dec 07 2015

%E a(11) from Kazuyoshi Asao, Feb 11 2002

%E a(12) from _Serge Batalov_, Dec 25 2015

%E a(13) from _Ben Meekins_, Feb 16 2016

%E a(14) from _Ben Meekins_, Dec 17 2016

%E a(15) from _Ben Meekins_, Sep 08 2018