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Numbers k such that (43*10^k - 403)/9 is prime.
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%I #53 May 25 2024 19:35:07

%S 1,2,3,6,11,20,23,24,26,36,56,224,411,543,611,1541,1632,3719,3888,

%T 4917,11454,24275,51816,58563,119024

%N Numbers k such that (43*10^k - 403)/9 is prime.

%C For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 7 followed by the digits 33 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 47w33</a>.

%e 3 is in this sequence because (43*10^3 - 403)/9 = 4733 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 3;

%e a(2) = 2, 433;

%e a(3) = 3, 4733;

%e a(4) = 6, 4777733;

%e a(5) = 11, 477777777733; etc.

%p select(k->isprime((43*10^k-403)/9),[$1..1000]); # _Muniru A Asiru_, Jan 05 2019

%t Select[Range[1, 100000], PrimeQ[(43*10^# - 403)/9] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Apr 24 2017

%E a(25) from _Robert Price_, Jan 04 2019