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Numbers k such that 2*10^k - 51 is prime.
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%I #15 May 05 2024 00:20:48

%S 2,3,4,8,11,13,17,28,56,105,231,339,643,922,1219,1880,2209,4238,4987,

%T 14770,56194,67043,96867,124751

%N Numbers k such that 2*10^k - 51 is prime.

%C For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 9 followed by the digits 49 is prime (see Example section).

%C a(25) > 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 19w49</a>.

%e 2 is in this sequence because 2*10^2 - 51 = 149 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 149;

%e a(2) = 3, 1949;

%e a(3) = 4, 19949;

%e a(4) = 8, 199999949;

%e a(5) = 11, 199999999949; etc.

%t Select[Range[2, 100000], PrimeQ[2*10^# - 51] &]

%o (PARI) isok(k) = isprime(2*10^k - 51); \\ _Michel Marcus_, Nov 20 2017

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Nov 19 2017

%E a(24) from _Robert Price_, Apr 13 2018