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Numbers k such that 33*10^k + 1 is prime.
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%I #15 May 02 2024 22:54:51

%S 1,2,5,6,7,8,29,47,145,205,227,505,553,600,787,809,1305,1447,1593,

%T 2285,4763,5679,9133,12516,14869,16536,33402,36085,51933,56443,69133

%N Numbers k such that 33*10^k + 1 is prime.

%C Numbers k such that the digits 33 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).

%C a(32) > 10^5.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 330w1</a>.

%e 5 is in this sequence because 33*10^5+1 = 3300001 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 331;

%e a(2) = 2, 3301;

%e a(3) = 5, 3300001;

%e a(4) = 6, 33000001;

%e a(5) = 7, 330000001;

%e a(6) = 8, 3300000001, etc.

%t Select[Range[0, 100000], PrimeQ[33*10^#+1] &]

%o (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime(33*10^n+1), print1(n, ", "))); \\ _Altug Alkan_, Mar 31 2016

%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A270974.

%K nonn,base,more

%O 1,2

%A _Robert Price_, Mar 30 2016