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Numbers k such that 28*10^k + 1 is prime.
0

%I #14 May 19 2024 21:55:21

%S 0,1,2,3,4,5,16,19,22,37,58,547,570,817,1068,1909,12809,14470,18209,

%T 33176,33412,42176,49798,89401

%N Numbers k such that 28*10^k + 1 is prime.

%C For k > 0, numbers k such that the digits 28 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).

%C a(25) > 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 280w1</a>.

%e 2 is in this sequence because 28*10^2 + 1 = 2801 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 29;

%e a(2) = 1, 281;

%e a(3) = 2, 2801;

%e a(4) = 3, 280001;

%e a(5) = 4, 2800001; etc.

%t Select[Range[0, 100000], PrimeQ[28*10^# + 1] &]

%o (PARI) lista(nn) = for(n = 0, nn, if(isprime(28*10^n+1), print1(n, ", "))) \\ _Iain Fox_, Oct 18 2017

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Oct 16 2017