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Search: id:A072180
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| A072180 |
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Numbers n such that 2^n - n^2 is prime. |
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+0
14
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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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The numbers corresponding to n = 2037, 2221, 3547 and 5515 have been certified prime with Primo. - Rick L. Shepherd (rshepherd2(AT)hotmail.com), Nov 10 2002
The remaining n's > 1000 correspond only to probable primes.
Certainly n must be odd. Let N(n) = 2^n - n^2. Additional restrictions come from the facts that 7 | N(n) if n is in {2, 4, 5, 6, 10, 15} mod 21 and 17 | N(n) if n is in {31, 57, 61, 71, 107, 109, 113, 131} mod 136. - Daniel Gronau, Jul 06 2002
Henri Lifchitz found the terms > 40000 in 2001, and 119087 in March 2002. - Hugo Pfoertner (hugo(AT)pfoertner.org), Nov 16 2004
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LINKS
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Henri Lifchitz, Renaud Lifchitz, PRP Top Records. 2^n-n^2.
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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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CROSSREFS
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Cf. A024012, A064539, A075896, A072164.
Adjacent sequences: A072177 A072178 A072179 this_sequence A072181 A072182 A072183
Sequence in context: A029667 A036708 A124822 this_sequence A024571 A068332 A029650
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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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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 01 2002
More terms from Hugo Pfoertner (hugo(AT)pfoertner.org), Nov 16 2004
More terms from Henri Lifchitz submitted by Ray Chandler (rayjchandler(AT)sbcglobal.net), Mar 02 2007
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