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A274678 Numbers k such that 7*10^k + 27 is prime.

%I A274678 #24 Apr 15 2024 16:22:41
%S A274678 1,2,3,5,7,34,38,49,51,89,91,132,227,3662,5019,9729,25437,99944,
%T A274678 106553,114577
%N A274678 Numbers k such that 7*10^k + 27 is prime.
%H A274678 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 70w27</a>.
%e A274678 3 is in this sequence because 7*10^3 + 27 = 7027 is prime.
%e A274678 4 is not in the sequence because 7*10^4 + 27 = 70027 = 239 * 293.
%e A274678 Initial terms and associated primes:
%e A274678 a(1) = 1: 97;
%e A274678 a(2) = 2: 727;
%e A274678 a(3) = 3: 7027;
%e A274678 a(4) = 5: 700027, etc.
%t A274678 Select[Range[0, 3000], PrimeQ[7 10^# + 27] &]
%o A274678 (Magma) [n: n in [1..800] | IsPrime(7*10^n+27)];
%o A274678 (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime(7*10^n+27), print1(n, ", "))); \\ _Altug Alkan_, Jul 05 2016
%o A274678 (Python)
%o A274678 from sympy import isprime
%o A274678 def afind(limit, startk=0):
%o A274678     sevenpow10 = 7*10**startk
%o A274678     for k in range(startk, limit+1):
%o A274678         if isprime(sevenpow10 + 27):
%o A274678             print(k, end=", ")
%o A274678         k += 1
%o A274678         sevenpow10 *= 10
%o A274678 afind(500) # _Michael S. Branicky_, Dec 31 2021
%Y A274678 Cf. similar sequences listed in A274676.
%K A274678 nonn,more
%O A274678 1,2
%A A274678 _Vincenzo Librandi_, Jul 04 2016
%E A274678 a(15)-a(16) from _Michael S. Branicky_, Dec 31 2021
%E A274678 a(17)-a(20) from Kamada data by _Tyler Busby_, Apr 14 2024