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A295403 Numbers k such that (41*10^k - 383)/9 is prime. 0

%I

%S 1,3,5,6,21,39,114,239,246,348,906,1115,2801,2958,2982,4275,6581,8736,

%T 27051,115523,124335

%N Numbers k such that (41*10^k - 383)/9 is prime.

%C For k > 1, numbers such that the digit 4 followed by k-2 occurrences of the digit 5 followed by the digits 13 is prime (see Example section).

%C a(22) > 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/primedifficulty.txt">Search for 45w13</a>

%e 3 is in this sequence because (41*10^3 - 383)/9 = 4513 is prime.

%e Initial terms and primes associated:

%e a(1) = 1, 3;

%e a(2) = 3, 4513;

%e a(3) = 5, 455513;

%e a(4) = 6, 4555513;

%e a(5) = 21, 4555555555555555555513; etc.

%t Select[Range[1, 100000], PrimeQ[(41*10^# - 383)/9] &]

%o (PARI) isok(k) = isprime((41*10^k - 383)/9); \\ _Michel Marcus_, Nov 22 2017

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Nov 21 2017

%E a(20)-a(21) from _Robert Price_, Nov 16 2018

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Last modified November 16 17:03 EST 2019. Contains 329201 sequences. (Running on oeis4.)