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A104072
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Primes of the form 2^n + 5^2.
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4
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29, 41, 89, 281, 1049, 1048601, 4194329, 17179869209, 1180591620717411303449, 4951760157141521099596496921, 5192296858534827628530496329220121, 332306998946228968225951765070086169
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OFFSET
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1,1
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COMMENTS
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Indeed, calculating mod 3 we have 2^n + 5^2 = (-1)^n + 1 = 0 if n is odd, so n must be even to yield a prime. - M. F. Hasler, Nov 13 2010
Those even values of n are given in A157006. Since n = 2k, these prime numbers also have the form 4^k + 25, where k is given in A204388. - Timothy L. Tiffin, Aug 06 2016
These primes a(m) can be used to generate numbers having deficiency 26. The formula a(m)*(a(m)-25)/2 produces those terms in A275702 having rightmost digit 8. - Timothy L. Tiffin, Aug 09 2016
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LINKS
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FORMULA
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If n == 0 mod 4, then a(m) == 1 mod 10. If n == 2 mod 4, then a(m) == 9 mod 10. - Timothy L. Tiffin, Aug 09 2016
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EXAMPLE
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a(1) = 2^2 + 5^2 = 4 + 25 = 29.
a(2) = 2^4 + 5^2 = 16 + 25 = 41.
a(3) = 2^6 + 5^2 = 64 + 25 = 89.
a(4) = 2^8 + 5^2 = 256 + 25 = 281.
a(5) = 2^10 + 5^2 = 1024 + 25 = 1049.
a(6) = 2^20 + 5^2 = 1048576 + 25 = 1048601. (End)
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MATHEMATICA
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a = Delete[Union[Flatten[Table[If [PrimeQ[2^n + 25] == True, 2^n + 25, 0], {n, 1, 400}]]], 1]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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