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Numbers k such that 7*10^k + 27 is prime.
1

%I #24 Apr 15 2024 16:22:41

%S 1,2,3,5,7,34,38,49,51,89,91,132,227,3662,5019,9729,25437,99944,

%T 106553,114577

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

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 70w27</a>.

%e 3 is in this sequence because 7*10^3 + 27 = 7027 is prime.

%e 4 is not in the sequence because 7*10^4 + 27 = 70027 = 239 * 293.

%e Initial terms and associated primes:

%e a(1) = 1: 97;

%e a(2) = 2: 727;

%e a(3) = 3: 7027;

%e a(4) = 5: 700027, etc.

%t Select[Range[0, 3000], PrimeQ[7 10^# + 27] &]

%o (Magma) [n: n in [1..800] | IsPrime(7*10^n+27)];

%o (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime(7*10^n+27), print1(n, ", "))); \\ _Altug Alkan_, Jul 05 2016

%o (Python)

%o from sympy import isprime

%o def afind(limit, startk=0):

%o sevenpow10 = 7*10**startk

%o for k in range(startk, limit+1):

%o if isprime(sevenpow10 + 27):

%o print(k, end=", ")

%o k += 1

%o sevenpow10 *= 10

%o afind(500) # _Michael S. Branicky_, Dec 31 2021

%Y Cf. similar sequences listed in A274676.

%K nonn,more

%O 1,2

%A _Vincenzo Librandi_, Jul 04 2016

%E a(15)-a(16) from _Michael S. Branicky_, Dec 31 2021

%E a(17)-a(20) from Kamada data by _Tyler Busby_, Apr 14 2024