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A271375 Numbers k such that (38*10^k + 637)/9 is prime.

%I A271375 #14 May 25 2024 15:04:46
%S A271375 1,4,14,19,25,26,32,41,59,79,83,101,103,200,308,314,548,565,620,922,
%T A271375 1102,1960,2245,2254,5393,5935,6227,14350,25070
%N A271375 Numbers k such that (38*10^k + 637)/9 is prime.
%C A271375 For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 2 followed by the digits 93 is prime (see Example section).
%C A271375 a(30) > 2*10^5.
%H A271375 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 42w93</a>.
%e A271375 4 is in this sequence because (38*10^4+637)/9 = 42293 is prime.
%e A271375 Initial terms and associated primes:
%e A271375 a(1) = 1, 113;
%e A271375 a(2) = 4, 42293;
%e A271375 a(3) = 14, 422222222222293;
%e A271375 a(4) = 19, 42222222222222222293;
%e A271375 a(5) = 25, 42222222222222222222222293, etc.
%t A271375 Select[Range[0, 100000], PrimeQ[(38*10^# + 637)/9] &]
%o A271375 (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime((38*10^n + 637)/9), print1(n, ", "))); \\ _Altug Alkan_, Apr 05 2016
%Y A271375 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A271375 nonn,more
%O A271375 1,2
%A A271375 _Robert Price_, Apr 05 2016