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A056206
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Smallest prime p such that p + 2^n is also a prime.
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13
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2, 3, 3, 3, 3, 5, 3, 3, 7, 11, 7, 5, 3, 17, 37, 3, 3, 29, 3, 53, 7, 17, 67, 11, 43, 41, 97, 29, 3, 11, 3, 11, 61, 17, 79, 53, 31, 29, 7, 23, 97, 71, 277, 29, 7, 59, 127, 5, 61, 191, 193, 101, 37, 5, 163, 3, 97, 131, 577, 131, 151, 197, 193, 29, 13, 131, 709, 3, 61
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OFFSET
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0,1
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LINKS
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FORMULA
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a(n) = Min{p|p+2^n=q, both p and q are primes}.
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EXAMPLE
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n=9, 512 + {2,3,5,7,11,...} = {514,515,519,523,...} = {2*257, 5*103, 11*47, 3*173, 523=prime, ...}. The smallest suitable prime is 11 and it gives 523 = 512 + 11. So a(9)=11.
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MAPLE
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a:= proc(n) option remember; local o, p; o, p:=2^n, 2;
while not isprime(o+p) do p:= nextprime(p) od; p
end:
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MATHEMATICA
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Table[i=1; While[!PrimeQ[2^n+(p=Prime[i])], i++]; p, {n, 0, 72}] (* Jayanta Basu, May 23 2013 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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