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A276511
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Primes that are equal to the sum of the prime factors of some perfect number.
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3
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OFFSET
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1,1
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COMMENTS
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Primes of the form 2^n + 2*n - 3 such that 2^n - 1 is also prime.
Conjectures (defining x = 170141183460469231731687303715884105727 = A007013(4)):
(1) 2^x + 2*x - 3 is in this sequence;
(2) a(5) = 2^x + 2*x - 3 (see comments of A276493);
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LINKS
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EXAMPLE
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a(1) = 5 because 2^2-1 = 3 and 2^2+2*2-3 = 5 are primes,
a(2) = 11 because 2^3-1 = 7 and 2^3+2*3-3 = 11 are primes,
a(3) = 139 because 2^7-1 = 127 and 2^7+2*7-3 = 139 are primes.
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MAPLE
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PROG
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(Magma) [2^n+2*n-3: n in [1..200] | IsPrime(2^n-1) and IsPrime(2^n+2*n-3)];
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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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