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A273006 Numbers k such that 88*10^k + 3 is prime.

%I A273006 #28 May 26 2024 14:58:18
%S A273006 1,2,3,7,19,21,31,50,55,151,167,287,542,603,926,1046,2066,2139,2651,
%T A273006 2787,5756,6028,6925,10135,13037,36476,74234,119295
%N A273006 Numbers k such that 88*10^k + 3 is prime.
%C A273006 For k > 0, numbers k such that the digits 88 followed by k-1 occurrences of the digit 0 followed by the digit 3 is prime (see Example section).
%C A273006 a(29) > 3*10^5.
%H A273006 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A273006 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 880w3</a>.
%e A273006 3 is in this sequence because 88*10^3 + 3 = 88003 is prime.
%e A273006 Initial terms and associated primes:
%e A273006 a(1) = 1, 883;
%e A273006 a(2) = 2, 8803;
%e A273006 a(3) = 3, 88003;
%e A273006 a(4) = 7, 880000003;
%e A273006 a(5) = 19, 880000000000000000003, etc.
%t A273006 Select[Range[0, 100000], PrimeQ[88*10^# + 3] &] (* Corrected by _Georg Fischer_, Jul 22 2019 *)
%o A273006 (PARI) is(n)=ispseudoprime(88*10^n + 3) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y A273006 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A273006 nonn,more
%O A273006 1,2
%A A273006 _Robert Price_, Nov 09 2016
%E A273006 a(28) from _Robert Price_, May 03 2020