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A072180
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Numbers k such that 2^k - k^2 is prime.
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18
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5, 7, 9, 17, 19, 51, 53, 81, 83, 119, 189, 219, 227, 301, 455, 461, 623, 2037, 2221, 2455, 3547, 5515, 6825, 8303, 9029, 12103, 49989, 55525, 64773, 80307, 119087, 141915, 192023, 205933, 301683, 307407
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OFFSET
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1,1
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COMMENTS
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The numbers corresponding to k = 2037, 2221, 3547 and 5515 have been certified prime with Primo. - Rick L. Shepherd, Nov 10 2002
The remaining k's > 1000 correspond only to probable primes.
Certainly k must be odd. Let N(k) = 2^k - k^2. Additional restrictions come from the facts that 7 | N(k) if k is in {2, 4, 5, 6, 10, 15} mod 21 and 17 | N(k) if k is in {31, 57, 61, 71, 107, 109, 113, 131} mod 136. - Daniel Gronau, Jul 06 2002
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LINKS
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MATHEMATICA
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Do[ If[ PrimeQ[ 2^n - n^2], Print[n]], {n, 1, 22850, 2}]
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PROG
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CROSSREFS
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KEYWORD
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hard,nonn
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AUTHOR
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Daniel Gronau (Daniel.Gronau(AT)gmx.de), Jun 30 2002
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EXTENSIONS
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STATUS
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approved
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