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Numbers k such that 34*10^k - 3 is prime.
0

%I #19 Jun 09 2024 18:05:56

%S 0,1,3,5,7,11,14,20,25,35,36,117,164,372,453,649,1743,1748,1897,2323,

%T 6351,16599,25017,25736,27866

%N Numbers k such that 34*10^k - 3 is prime.

%C For k > 0, numbers k such that the digits 33 followed by k-1 occurrences of the digit 9 followed by the digit 7 is prime (see Example section).

%C a(26) > 2*10^5.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 339w7</a>.

%e 3 is in this sequence because 34*10^3 - 3 = 33997 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 31;

%e a(2) = 1, 337;

%e a(3) = 3, 33997;

%e a(4) = 5, 3399997;

%e a(5) = 7, 339999997; etc.

%t Select[Range[0, 100000], PrimeQ[34*10^# - 3] &]

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Feb 21 2017