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A273679 Numbers k such that 10^k - 1000000001 is prime.

%I A273679 #27 May 31 2024 21:04:26
%S A273679 11,18,22,26,27,36,45,59,140,162,201,278,427,563,588,757,951,2006,
%T A273679 3938,4127,4490,5637,6074,6725,7025,10191,25628,39415,51872,57501,
%U A273679 90227,115773,117142,148934
%N A273679 Numbers k such that 10^k - 1000000001 is prime.
%C A273679 For k > 9, numbers k such that k-10 occurrences of the digit 9 followed by the digits 8999999999 is prime (see Example section).
%C A273679 a(35) > 2*10^5.
%H A273679 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A273679 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 9w8999999999</a>.
%e A273679 11 is in this sequence because 10^11 - 1000000001 = 98999999999 is prime.
%e A273679 Initial terms and associated primes:
%e A273679 a(1) = 11, 98999999999,
%e A273679 a(2) = 18, 999999998999999999,
%e A273679 a(3) = 22, 9999999999998999999999,
%e A273679 a(4) = 26, 99999999999999998999999999,
%e A273679 a(5) = 27, 999999999999999998999999999, etc.
%t A273679 Select[Range[0, 100000], PrimeQ[10^#-1000000001] &]
%o A273679 (PARI) is(n)=ispseudoprime(10^n-10^9-1) \\ _Charles R Greathouse IV_, Jun 08 2016
%o A273679 (Python)
%o A273679 from sympy import isprime
%o A273679 def afind(limit):
%o A273679     tenk = 10**10
%o A273679     for k in range(10, limit+1):
%o A273679         if isprime(tenk - 1000000001): print(k, end=", ")
%o A273679         tenk *= 10
%o A273679 afind(100000) # _Michael S. Branicky_, Nov 18 2021
%Y A273679 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A273679 nonn,more
%O A273679 1,1
%A A273679 _Robert Price_, May 27 2016
%E A273679 a(32)-a(33) from _Robert Price_, Mar 01 2018
%E A273679 a(34) from _Robert Price_, Dec 31 2020