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Numbers k such that 8*10^k + 81 is prime.
0

%I #12 Jun 09 2024 22:02:06

%S 0,2,3,9,11,26,39,42,58,75,105,167,279,561,2152,2378,3774,5001,5736,

%T 9470,13419,14535,32291,89800,146421

%N Numbers k such that 8*10^k + 81 is prime.

%C For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 0 followed by the digits 81 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 80w81</a>.

%e 3 is in this sequence because 8*10^3 + 81 = 8081 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 89;

%e a(2) = 2, 881;

%e a(3) = 3, 8081;

%e a(4) = 9, 8000000081;

%e a(5) = 11, 800000000081; etc.

%t Select[Range[0, 100000], PrimeQ[(8*10^# + 81] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, May 29 2017

%E a(25) from _Robert Price_, Aug 22 2019