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Numbers k such that (38*10^k + 637)/9 is prime.
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%I #14 May 25 2024 15:04:46

%S 1,4,14,19,25,26,32,41,59,79,83,101,103,200,308,314,548,565,620,922,

%T 1102,1960,2245,2254,5393,5935,6227,14350,25070

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

%C 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 a(30) > 2*10^5.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 42w93</a>.

%e 4 is in this sequence because (38*10^4+637)/9 = 42293 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 113;

%e a(2) = 4, 42293;

%e a(3) = 14, 422222222222293;

%e a(4) = 19, 42222222222222222293;

%e a(5) = 25, 42222222222222222222222293, etc.

%t Select[Range[0, 100000], PrimeQ[(38*10^# + 637)/9] &]

%o (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime((38*10^n + 637)/9), print1(n, ", "))); \\ _Altug Alkan_, Apr 05 2016

%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

%K nonn,more

%O 1,2

%A _Robert Price_, Apr 05 2016