login
Numbers k such that 10^k - 201 is prime.
2

%I #23 May 03 2024 15:42:24

%S 13,20,40,43,73,85,576,1676,33565

%N Numbers k such that 10^k - 201 is prime.

%C For k > 2, numbers k such that k-3 occurrences of the digit 9 followed by the digits 799 is prime.

%C a(9) > 10000. - _Robert G. Wilson v_, Nov 24 2016

%H Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.

%e 13 is in this sequence because 10^13 - 201 = 9999999999799 is prime.

%e Initial terms and associated primes:

%e a(1) = 13, 9999999999799;

%e a(2) = 20, 99999999999999999799;

%e a(3) = 40, 9999999999999999999999999999999999999799; etc.

%p A278470:=n->`if`(isprime(10^n-201), n, NULL): seq(A278470(n), n=1..10^3); # _Wesley Ivan Hurt_, Dec 08 2016

%t Select[Range[3, 2000], PrimeQ[10^# - 201] &]

%o (Magma) [n: n in [3..500] | IsPrime(10^n-201)];

%o (PARI) is(n)=ispseudoprime(10^n-201) \\ _Charles R Greathouse IV_, Jun 06 2017

%Y Cf. A108327 (10^n-21), this sequence (10^n-201), A278397 (10^n-20001), A278471 (10^n-2001).

%K nonn,more

%O 1,1

%A _Vincenzo Librandi_, Nov 23 2016

%E a(9) from Kamada data by _Tyler Busby_, May 03 2024