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A270974 Numbers k such that 7*10^k + 57 is prime.

%I A270974 #23 May 25 2024 19:39:26
%S A270974 1,2,3,5,6,7,12,14,19,21,27,33,60,61,91,102,535,549,614,695,709,1014,
%T A270974 2448,2519,3464,3511,6348,6841,11009,11177,20754,26610,30651,39246,
%U A270974 122294
%N A270974 Numbers k such that 7*10^k + 57 is prime.
%C A270974 For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 0 followed by the digits 57 is prime (see Example section).
%C A270974 a(35) > 2*10^5.
%H A270974 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 70w57</a>.
%e A270974 3 is in this sequence because 7*10^3+57 = 7057 is prime.
%e A270974 Initial terms and associated primes:
%e A270974 a(1) = 1, 127;
%e A270974 a(2) = 2, 757;
%e A270974 a(3) = 3, 7057;
%e A270974 a(4) = 5, 700057;
%e A270974 a(5) = 6, 7000057;
%e A270974 a(6) = 7, 70000057, etc.
%t A270974 Select[Range[0, 100000], PrimeQ[7*10^# + 57] &]
%o A270974 (PARI) lista(nn) = {for(n=1, nn, if(ispseudoprime(7*10^n + 57), print1(n, ", ")));} \\ _Altug Alkan_, Mar 27 2016
%o A270974 (Magma) [n: n in [1..500] | IsPrime(7*10^n + 57)]; // _Vincenzo Librandi_, Jul 03 2016
%Y A270974 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929.
%K A270974 nonn,more
%O A270974 1,2
%A A270974 _Robert Price_, Mar 27 2016
%E A270974 a(35) from _Robert Price_, Jun 13 2019