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Numbers k such that (26*10^k - 503)/9 is prime.
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%I #13 May 02 2024 07:19:59

%S 2,3,5,15,23,32,38,60,239,279,396,599,797,4341,7041,10103,20496,24285,

%T 33156,46694,49427,51537,104132,116999,151391

%N Numbers k such that (26*10^k - 503)/9 is prime.

%C For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 8 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 28w33</a>.

%e 2 is in this sequence because (26*10^2 - 503)/9 = 233 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 233;

%e a(2) = 3, 2833;

%e a(3) = 5, 288833;

%e a(4) = 15, 2888888888888833;

%e a(5) = 23, 288888888888888888888833; etc.

%t Select[Range[2, 100000], PrimeQ[(26*10^# - 503)/9] &]

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Dec 03 2017

%E a(23)-a(25) from _Robert Price_, Jul 04 2018