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Numbers k such that (55*10^k + 377)/9 is prime.
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%I #11 May 26 2024 23:00:28

%S 1,2,4,20,40,61,62,82,169,172,214,874,1520,1652,2185,3221,4012,4669,

%T 13165,18922,91142,106222

%N Numbers k such that (55*10^k + 377)/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 53 is prime (see Example section).

%C a(23) > 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 61w53</a>.

%e 2 is in this sequence because (55*10^2 + 377)/9 = 653 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 103;

%e a(2) = 2, 653;

%e a(3) = 4, 61153;

%e a(4) = 20, 611111111111111111153;

%e a(5) = 40, 61111111111111111111111111111111111111153; etc.

%t Select[Range[0, 100000], PrimeQ[(55*10^# + 377)/9] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Oct 25 2017

%E a(22) from _Robert Price_, Feb 27 2019