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A278397 Numbers k such that 10^k - 20001 is prime.

%I A278397 #22 May 31 2024 22:11:38
%S A278397 5,11,16,21,37,83,94,299,318,467,622,707,1931,2175,2189,2238,2526,
%T A278397 5202,10541,15822,17407,19919,19998,25407,96377,118009
%N A278397 Numbers k such that 10^k - 20001 is prime.
%C A278397 For k > 4, numbers k such that k-5 occurrences of the digit 9 followed by the digits 79999 is prime (see Example section).
%C A278397 a(27) > 2*10^5.
%H A278397 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A278397 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 9w79999</a>.
%e A278397 5 is in this sequence because 10^5 - 20001 = 79999 is prime.
%e A278397 Initial terms and associated primes:
%e A278397 a(1) = 5, 79999;
%e A278397 a(2) = 11, 99999979999;
%e A278397 a(3) = 16, 9999999999979999;
%e A278397 a(4) = 21, 999999999999999979999;
%e A278397 a(5) = 37, 9999999999999999999999999999999979999; etc.
%t A278397 Select[Range[0, 100000], PrimeQ[10^# - 20001] &]
%o A278397 (Magma) [n: n in [5..400] | IsPrime(10^n - 20001)]; // _Vincenzo Librandi_, Nov 21 2016
%o A278397 (PARI) is(n)=ispseudoprime(10^n-20001) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y A278397 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A278397 nonn,more,hard
%O A278397 1,1
%A A278397 _Robert Price_, Nov 20 2016
%E A278397 a(26) from _Robert Price_, Jan 26 2018