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A274519
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Numbers k for which 4^k - 27 is prime.
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3
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3, 4, 5, 10, 11, 13, 25, 28, 29, 65, 70, 115, 305, 515, 2029, 2393, 2605, 3530, 4036, 4750, 10288, 11048, 11596
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OFFSET
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1,1
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COMMENTS
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The prime numbers that these exponents generate are given in A275750.
Since 4^(6k) - 27 = 4096^k - 27 == (1^k - 27) mod 13 = -26 mod 13 == 0 mod 13, no multiple of 6 will be in this sequence. Also, since 4^(5k+2) - 27 = 16*1024^k - 27 == (16*1^k - 27) mod 11 = -11 mod 11 == 0 mod 11, no number congruent to 2 mod 5 will be in this sequence.
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LINKS
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EXAMPLE
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a(1) = 3, since 4^3 - 27 = 64 - 27 = 37, which is prime.
a(2) = 4, since 4^4 - 27 = 256 - 27 = 229, which is prime.
a(3) = 5, since 4^5 - 27 = 1024 - 27 = 997, which is prime.
a(4) = 10, since 4^10 - 27 = 1048576 - 27 = 1048549, which is prime.
a(5) = 11, since 4^11 - 27 = 4194304 - 27 = 4194277, which is prime.
a(6) = 13, since 4^13 - 27 = 67108864 - 27 = 67108837, which is prime.
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MATHEMATICA
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PROG
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(Python)
from sympy import isprime
def afind(limit, startk=3):
alst, pow4 = [], 4**startk
for k in range(startk, limit+1):
if isprime(pow4 - 27): print(k, end=", ")
pow4 *= 4
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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