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A117588
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Numbers k such that 2^k + prime(k)^2 is prime.
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0
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2, 6, 8, 14, 20, 90, 102, 154, 228, 310, 418, 554, 1070, 1224, 3144, 3996, 4464, 16194, 17096, 36642
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OFFSET
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1,1
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COMMENTS
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All terms are even since 2^k + prime(k)^2 == 0 (mod 3) for any odd number k. - Robert G. Wilson v, Apr 03 2006
If k is odd, prime(k) == +- 1 (mod 3) making prime(k)^2 == 1 (mod 3) and 2^k == - 1 (mod 3). - Robert G. Wilson v, Apr 03 2006
No more terms below 30000.
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LINKS
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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) then n else fi end: seq(a(n), n=1..1300); # Emeric Deutsch, 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, Apr 03 2006 *)
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PROG
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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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KEYWORD
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nonn,more
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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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STATUS
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approved
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