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A064539
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Numbers n such that 2^n + n^2 is prime.
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6
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1, 3, 9, 15, 21, 33, 2007, 2127, 3759, 29355, 34653, 57285, 99069, 1933695
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OFFSET
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1,2
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COMMENTS
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Values 2^2007+2007^2, 2^2127+2127^2, 2^3759+3759^2 were proved prime with Primo.
n is always an odd multiple of 3 (except for the first term), i.e., a(n) is a subsequence of A016945. - Lekraj Beedassy, Jan 01 2007
Some of the results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 14 2019
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REFERENCES
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J.-M. De Koninck & A. Mercier, 1001 Problemes en Theorie Classique Des Nombres, Problem 165 pp. 30, 160, Ellipses Paris 2004.
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LINKS
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PROG
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(PARI) for(n=1, 5000, if(isprime(2^n+n^2), print(n)))
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CROSSREFS
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KEYWORD
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nonn,more,hard
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AUTHOR
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EXTENSIONS
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a(14) from Ryan Propper, May 11 2023. n=1933695 corresponds to a probable prime with 582101 digits, and was PRP tested with PFGW.
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STATUS
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approved
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