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Numbers k such that 44*10^k + 3 is prime.
0

%I #15 Jun 09 2024 22:01:33

%S 0,1,6,7,27,51,67,69,115,153,346,351,1152,1807,2508,4470,4875,5277,

%T 7527,10339,11407,21807,26199,46473,68368,181029

%N Numbers k such that 44*10^k + 3 is prime.

%C For k > 0, numbers k such that the digits 44 followed by k-1 occurrences of the digit 0 followed by the digit 3 is prime (see Example section).

%C a(29) > 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 440w3</a>.

%e 1 is in this sequence because 44*10^1 + 3 = 443 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 47;

%e a(2) = 1, 443;

%e a(3) = 6, 44000003;

%e a(4) = 7, 440000003;

%e a(5) = 27, 44000000000000000000000000003; etc.

%t Select[Range[0, 100000], PrimeQ[44*10^# + 3] &]

%o (PARI) isok(k) = ispseudoprime(44*10^k + 3) \\ _Altug Alkan_, Aug 27 2017

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Aug 27 2017

%E a(28) from _Robert Price_, Apr 09 2020