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Numbers k such that (55*10^k + 89)/9 is prime.
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%I #12 May 26 2024 22:59:04

%S 1,3,4,7,10,31,39,70,84,135,154,279,282,522,660,765,1153,1980,5670,

%T 8064,20823,34290,79711,109759

%N Numbers k such that (55*10^k + 89)/9 is prime.

%C For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 1 followed by the digits 21 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 61w21</a>.

%e 3 is in this sequence because (55*10^3 + 89)/9 = 6121 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 71;

%e a(2) = 3, 6121;

%e a(3) = 4, 61121;

%e a(4) = 7, 61111121;

%e a(5) = 10, 61111111121; etc.

%t Select[Range[0, 100000], PrimeQ[(55*10^# + 89)/9] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Sep 04 2017

%E a(24) from _Robert Price_, Mar 01 2019