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Numbers k such that (56*10^k + 223)/9 is prime.
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%I #18 May 25 2024 19:39:38

%S 0,2,3,5,8,32,36,53,92,126,156,158,536,639,846,1356,1953,2237,4407,

%T 5082,17447,17922,24806,25926,29699,30474,37424,63942

%N Numbers k such that (56*10^k + 223)/9 is prime.

%C For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 2 followed by the digits 47 is prime (see Example section).

%C a(29) > 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 62w47</a>.

%e 3 is in this sequence because (56*10^3 + 223)/9 = 6247 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 31;

%e a(2) = 2, 647;

%e a(3) = 3, 6247;

%e a(4) = 5, 622247;

%e a(5) = 8, 622222247, etc.

%t Select[Range[0, 100000], PrimeQ[(56*10^# + 223)/9] &]

%o (Magma) [n: n in [0..500] | IsPrime((56*10^n+223) div 9)]; // _Vincenzo Librandi_, Aug 01 2016

%o (PARI) is(n)=ispseudoprime((56*10^n+223)/9) \\ _Charles R Greathouse IV_, Jun 13 2017

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

%K nonn,more

%O 1,2

%A _Robert Price_, Jul 31 2016