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Numbers k such that 3*10^k + 59 is prime.
0

%I #20 May 27 2024 07:15:46

%S 1,2,4,7,18,19,22,26,36,46,49,64,82,121,1204,1716,2359,4541,7194,8095,

%T 14857,18596,27648,37066,109861,171391

%N Numbers k such that 3*10^k + 59 is prime.

%C For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 0 followed by the digits 59 is prime (see Example section).

%C a(27) > 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 30w59</a>.

%e 4 is in this sequence because 3*10^4 + 59 = 30059 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 89;

%e a(2) = 2, 359;

%e a(3) = 4, 30059;

%e a(4) = 7; 30000059;

%e a(5) = 18, 3000000000000000059; etc.

%t Select[Range[0, 100000], PrimeQ[3*10^# + 59] &]

%o (PARI) isok(k) = ispseudoprime(3*10^k + 59) \\ _Altug Alkan_, Aug 13 2017

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Aug 13 2017

%E a(25)-a(26) from _Robert Price_, Aug 25 2018