cp's OEIS Frontend

A275096 Numbers k such that 2*10^k + 89 is prime.

%I A275096 #19 May 02 2024 04:23:09
%S A275096 1,3,4,8,9,10,13,20,27,74,89,93,137,139,296,310,662,749,1249,2540,
%T A275096 2848,3309,8677,11573,15286,17125,39526,42187,44476,47823,92897
%N A275096 Numbers k such that 2*10^k + 89 is prime.
%C A275096 For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 0 followed by the digits 89 is prime (see Example section).
%C A275096 a(32) > 10^5.
%H A275096 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A275096 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 20w89</a>.
%e A275096 3 is in this sequence because 2*10^3 + 89 = 2089 is prime.
%e A275096 Initial terms and associated primes:
%e A275096 a(1) = 1, 109;
%e A275096 a(2) = 3, 2089;
%e A275096 a(3) = 4, 20089;
%e A275096 a(4) = 8, 200000089;
%e A275096 a(5) = 9, 2000000089, etc.
%t A275096 Select[Range[0, 100000], PrimeQ[2*10^# + 89] &]
%o A275096 (Magma) [n: n in [1..500] | IsPrime(2*10^n+89)]; // _Vincenzo Librandi_, Jul 17 2016
%o A275096 (PARI) is(n)=ispseudoprime(2*10^n+89) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y A275096 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A275096 nonn,more
%O A275096 1,2
%A A275096 _Robert Price_, Jul 16 2016