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A294909 Numbers k such that (10^k + 47)/3 is prime.

%I A294909 #27 May 18 2024 11:33:10
%S A294909 1,3,5,6,9,13,120,220,568,640,666,1205,1600,2479,2482,2939,3077,8649,
%T A294909 9520,12407,33421,36162,41190,65340
%N A294909 Numbers k such that (10^k + 47)/3 is prime.
%C A294909 For k > 1, numbers k such that k-2 occurrences of the digit 3 followed by the digits 49 is prime (see Example section). - _Robert Price_, Nov 10 2017
%C A294909 a(25) > 3*10^5. - _Robert Price_, Oct 26 2023
%H A294909 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A294909 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 3w49</a>.
%e A294909 3 is in this sequence because (10^3 + 47)/3 = 349 is prime.
%e A294909 Initial terms and associated primes:
%e A294909 a(1) = 1, 19;
%e A294909 a(2) = 3, 349;
%e A294909 a(3) = 5, 33349;
%e A294909 a(4) = 6, 333349;
%e A294909 a(5) = 9, 333333349; etc.
%t A294909 Select[Range[0, 100000], PrimeQ[(10^# + 47)/3] &]
%o A294909 (Magma) [n: n in [0..500] |IsPrime((10^n+47) div 3)];
%o A294909 (PARI) is(n) = ispseudoprime((10^n + 47) / 3); \\ _Altug Alkan_, Sep 26 2016
%Y A294909 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%Y A294909 See also similar sequences listed in A274986.
%K A294909 nonn,more,hard
%O A294909 1,2
%A A294909 _Vincenzo Librandi_, Sep 26 2016
%E A294909 a(18)-a(24) from _Robert Price_, Nov 10 2017