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A097058
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Numbers of the form p^2 + 2^p for p prime.
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3
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8, 17, 57, 177, 2169, 8361, 131361, 524649, 8389137, 536871753, 2147484609, 137438954841, 2199023257233, 8796093024057, 140737488357537, 9007199254743801, 576460752303426969, 2305843009213697673, 147573952589676417417, 2361183241434822611889
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OFFSET
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1,1
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COMMENTS
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For any n>=3, a(n) is divisible by 3. This follows from the following simple result, combined with the fact that A061725(n), n>=3, is divisible by 3: Let r>=5 be an odd integer such that r^2 + 2 is divisible by 3. Then r^2 + 2^i is divisible by 3 for any odd integer i>=3. In particular, r^2 + 2^r is divisible by 3. This contribution was inspired by Problem of the Month - Math Central, MP98 (problem for October 2010), which asks for all primes p such that 2^p + p^2 is also a prime. - Shai Covo (green355(AT)netvision.net.il), Nov 02 2010
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LINKS
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EXAMPLE
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For example, the first two terms are 2^2 + 2^2 = 8, 3^2 + 2^3 = 17
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MAPLE
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a:= proc(n) local p; p:= ithprime(n); p^2+2^p end:
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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