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A274677
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Numbers k such that 7*10^k + 19 is prime.
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1
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1, 2, 3, 4, 27, 32, 63, 69, 107, 145, 154, 173, 190, 271, 412, 1219, 1509, 2392, 4444, 5567, 7424, 32174, 51573
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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EXAMPLE
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3 is in this sequence because 7*10^3 + 19 = 7019 is prime.
5 is not in the sequence because 7*10^5 + 19 = 79*8861.
Initial terms and associated primes:
a(1) = 1: 89;
a(2) = 2: 719;
a(3) = 3: 7019;
a(4) = 4: 70019, etc.
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MATHEMATICA
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Select[Range[0, 3000], PrimeQ[7 10^# + 19] &]
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PROG
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(Magma) [n: n in [1..800] | IsPrime(7*10^n+19)];
(PARI) lista(nn) = for(n=1, nn, if(ispseudoprime(7*10^n+19), print1(n, ", "))); \\ Altug Alkan, Jul 05 2016
(Python)
from sympy import isprime
def afind(limit, startk=0):
sevenpow10 = 7*10**startk
for k in range(startk, limit+1):
if isprime(sevenpow10 + 19):
print(k, end=", ")
k += 1
sevenpow10 *= 10
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CROSSREFS
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Cf. similar sequences listed in A274676.
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KEYWORD
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nonn,more,changed
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AUTHOR
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EXTENSIONS
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a(22)-a(23) from Kamada data by Tyler Busby, Apr 14 2024
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STATUS
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approved
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