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Least number k such that 10^(n+k) - 10^n - 1 is prime.
4

%I #24 Aug 12 2024 18:36:09

%S 1,10,1,2,2,3,1,6,2,20,3,4,30,9,4,5,14,4,1,658,6,10,32,9,2,9,109,8,1,

%T 7,12,6,4,2,5,137,1,15,112,30,237,83,12,21,5,4,20,15,42,3,16,41,26,60,

%U 157,8,16,76,69,10,4,4,120,39,8,7,115,22,14,2,102

%N Least number k such that 10^(n+k) - 10^n - 1 is prime.

%C Near repdigit primes: concatenation of k-1 9's, one 8, and n 9's.

%H Pierre CAMI, <a href="/A213790/b213790.txt">Table of n, a(n) for n = 1..1100</a>

%e (10^1-1)*10^1-1 = 89 prime so a(1) = 1.

%e (10^10-1)*10^2-1 = 999999999899 prime so a(2) = 10.

%t lnk[n_]:=Module[{k=1,c=10^n+1},While[!PrimeQ[10^(n+k)-c],k++];k]; Array[lnk,80] (* _Harvey P. Dale_, Aug 12 2024 *)

%o (PARI) a(n) = {my(k=1); while (!ispseudoprime(10^(n+k) - 10^n - 1), k++); k;} \\ _Michel Marcus_, Sep 21 2019

%K nonn

%O 1,2

%A _Pierre CAMI_, Jun 20 2012