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A275524 Numbers k such that (56*10^k + 223)/9 is prime.

%I A275524 #18 May 25 2024 19:39:38
%S A275524 0,2,3,5,8,32,36,53,92,126,156,158,536,639,846,1356,1953,2237,4407,
%T A275524 5082,17447,17922,24806,25926,29699,30474,37424,63942
%N A275524 Numbers k such that (56*10^k + 223)/9 is prime.
%C A275524 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 A275524 a(29) > 10^5.
%H A275524 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A275524 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 62w47</a>.
%e A275524 3 is in this sequence because (56*10^3 + 223)/9 = 6247 is prime.
%e A275524 Initial terms and associated primes:
%e A275524 a(1) = 0, 31;
%e A275524 a(2) = 2, 647;
%e A275524 a(3) = 3, 6247;
%e A275524 a(4) = 5, 622247;
%e A275524 a(5) = 8, 622222247, etc.
%t A275524 Select[Range[0, 100000], PrimeQ[(56*10^# + 223)/9] &]
%o A275524 (Magma) [n: n in [0..500] | IsPrime((56*10^n+223) div 9)]; // _Vincenzo Librandi_, Aug 01 2016
%o A275524 (PARI) is(n)=ispseudoprime((56*10^n+223)/9) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y A275524 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A275524 nonn,more
%O A275524 1,2
%A A275524 _Robert Price_, Jul 31 2016