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A097058
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Numbers of the form p^2 + 2^p for p prime.
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2
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8, 17, 57, 177, 2169, 8361, 131361, 524649, 8389137, 536871753, 2147484609, 137438954841, 2199023257233, 8796093024057, 140737488357537, 9007199254743801, 576460752303426969, 2305843009213697673
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Contribution from Shai Covo (green355(AT)netvision.net.il), Nov 02 2010: (Start)
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. (End)
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EXAMPLE
| For example, the first two terms are 2^2 + 2^2 = 8, 3^2 + 2^3 = 17
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MATHEMATICA
| Table[ Prime[n]^2 + 2^Prime[n], {n, 16}] (from Robert G. Wilson v Sep 15 2004)
#^2+2^#&/@Prime[Range[20]] (* From Harvey P. Dale, Jul 12 2011 *)
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PROG
| (PARI) forprime(p=2, 61, print1(p^2+2^p, ", ")) (Brockhaus)
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CROSSREFS
| Sequence in context: A173056 A008782 A146078 * A186255 A187987 A171065
Adjacent sequences: A097055 A097056 A097057 * A097059 A097060 A097061
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KEYWORD
| nonn,easy
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AUTHOR
| Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Sep 15 2004
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EXTENSIONS
| More terms from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Ray Chandler (rayjchandler(AT)sbcglobal.net) and Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 15 2004
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