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A274677 Numbers k such that 7*10^k + 19 is prime.

%I A274677 #29 Apr 15 2024 03:15:21
%S A274677 1,2,3,4,27,32,63,69,107,145,154,173,190,271,412,1219,1509,2392,4444,
%T A274677 5567,7424,32174,51573
%N A274677 Numbers k such that 7*10^k + 19 is prime.
%C A274677 No term is divisible by 6 (A047253) because 7*1000000^k + 19 = 7*(76923*13 + 1)^k + 19 is divisible by 13 and is therefore not prime. - _Bruno Berselli_, Jul 05 2016
%H A274677 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 70w19</a>.
%e A274677 3 is in this sequence because 7*10^3 + 19 = 7019 is prime.
%e A274677 5 is not in the sequence because 7*10^5 + 19 = 79*8861.
%e A274677 Initial terms and associated primes:
%e A274677 a(1) = 1: 89;
%e A274677 a(2) = 2: 719;
%e A274677 a(3) = 3: 7019;
%e A274677 a(4) = 4: 70019, etc.
%t A274677 Select[Range[0, 3000], PrimeQ[7 10^# + 19] &]
%o A274677 (Magma) [n: n in [1..800] | IsPrime(7*10^n+19)];
%o A274677 (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime(7*10^n+19), print1(n, ", "))); \\ _Altug Alkan_, Jul 05 2016
%o A274677 (Python)
%o A274677 from sympy import isprime
%o A274677 def afind(limit, startk=0):
%o A274677     sevenpow10 = 7*10**startk
%o A274677     for k in range(startk, limit+1):
%o A274677         if isprime(sevenpow10 + 19):
%o A274677             print(k, end=", ")
%o A274677         k += 1
%o A274677         sevenpow10 *= 10
%o A274677 afind(500) # _Michael S. Branicky_, Dec 31 2021
%Y A274677 Subsequence of A047253.
%Y A274677 Cf. similar sequences listed in A274676.
%K A274677 nonn,more
%O A274677 1,2
%A A274677 _Vincenzo Librandi_, Jul 04 2016
%E A274677 a(20)-a(21) from _Michael S. Branicky_, Dec 31 2021
%E A274677 a(22)-a(23) from Kamada data by _Tyler Busby_, Apr 14 2024