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Numbers k such that 3*10^k + 89 is prime.
0

%I #58 Jun 02 2024 14:03:46

%S 2,3,4,5,6,8,10,14,15,62,98,184,190,389,430,815,918,1124,1284,9544,

%T 10068,16514,24756,39880,86478,179138

%N Numbers k such that 3*10^k + 89 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 89 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 30w89</a>.

%e 3 is in this sequence because 3*10^3 + 89 = 3089 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 389;

%e a(2) = 3, 3089;

%e a(3) = 4, 30089;

%e a(4) = 5, 300089;

%e a(5) = 6, 3000089; etc.

%t Select[Range[0, 100000], PrimeQ[3*10^# + 89] &]

%o (PARI) isok(k) = ispseudoprime(3*10^k + 89); \\ _Altug Alkan_, Mar 30 2018

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Mar 23 2017

%E a(26) from _Robert Price_, Oct 22 2018