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Search: id:A117588
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| A117588 |
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Numbers n such that 2^n + prime(n)^2 is prime. |
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+0
1
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| 2, 6, 8, 14, 20, 90, 102, 154, 228, 310, 418, 554, 1070, 1224, 3144, 3996, 4464, 16194, 17096
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n) is always even since for any odd number k, 2^k+prime(k)^2 == 0 (mod 3). - Robert G. Wilson v (rgwv(at)rgwv.com) Apr 03 2006
If k is odd, prime(k) is either == +/- 1 (mod 3) making prime(k)^2 == 1 (mod 3) and 2^k is - 1 (mod 3). - Robert G. Wilson v (rgwv(at)rgwv.com) Apr 03 2006
No more terms below 30000.
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EXAMPLE
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20 is in the sequence because the 20th prime is 71 and 2^20+71^2=1053617 is prime.
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MAPLE
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a:=proc(n) if isprime(2^n+ithprime(n)^2)=true then n else fi end: seq(a(n), n=1..1300); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 06 2006
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MATHEMATICA
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Do[ If[ PrimeQ[2^n + Prime[n]^2], Print[n]], {n, 20000}] (* Robert G. Wilson v *)
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PROGRAM
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(PARI) for(i=1, 3000, if(isprime(2^i+prime(i)^2), print1(i, ", ")))
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CROSSREFS
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Sequence in context: A063242 A104636 A137831 this_sequence A022112 A107019 A048133
Adjacent sequences: A117585 A117586 A117587 this_sequence A117589 A117590 A117591
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KEYWORD
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nonn
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AUTHOR
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Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Apr 03 2006
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EXTENSIONS
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a(15)-a(19) from Robert G. Wilson v (rgwv(at)rgwv.com) and Giovanni Resta (g.resta(AT)iit.cnr.it), Apr 03 2006
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