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Numbers k such that 5*10^k + 81 is prime.
1

%I #17 May 26 2024 22:59:50

%S 1,3,6,16,30,33,36,37,85,288,561,805,850,1057,1192,1312,2571,4579,

%T 5223,5940,10191,18756,24564,29595,43891,65905,89118,97963,112003,

%U 139945,174101,195221

%N Numbers k such that 5*10^k + 81 is prime.

%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 0 followed by the digits 81 is prime (see Example section).

%C a(33) > 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 50w81</a>.

%e 3 is in this sequence because 5*10^3 + 81 = 5081 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 131;

%e a(2) = 3, 5081;

%e a(3) = 6, 5000081;

%e a(4) = 16, 50000000000000081;

%e a(5) = 30, 5000000000000000000000000000081; etc.

%t Select[Range[0, 100000], PrimeQ[5*10^# + 81] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Aug 27 2017

%E a(29)-a(32) from _Robert Price_, Mar 04 2019

%E Terms reordered into ascending order by _Robert Price_, Apr 03 2022