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Search: id:A052007
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| A052007 |
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Numbers n such that 2^n + n is prime. |
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+0
7
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| 1, 3, 5, 9, 15, 39, 75, 81, 89, 317, 701, 735, 1311, 1881, 3201, 3225, 11795, 88071, 204129, 678561
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Terms >= 701 are currently only strongpseudoprime.
If n=1 (mod 6) or n=2 (mod 6) then 3 divides 2^n+n. Thus for n > 1, a(n)!=1 (mod 6) and a(n)!=2 (mod 6). The next term is greater than 20000 with the next prime having more than 6020 digits.
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LINKS
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Henri Lifchitz, Renaud Lifchitz, PRP Top Records. 2^n+n.
Primeform: User group for PFGW & PrimeForm programs.
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EXAMPLE
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2^39 + 39 = 549755813927 is prime.
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MATHEMATICA
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Do[ If[ PrimeQ[ 2^n + n ], Print[ n ] ], {n, 0, 7000} ]
v={1}; Do[If[Mod[n, 2]*(Mod[n, 6]-1)!= 0&&PrimeQ[2^n+n], v=Append[v, n]; Print[v]], {n, 2, 20000}]
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CROSSREFS
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Cf. A006127, A048744.
Adjacent sequences: A052004 A052005 A052006 this_sequence A052008 A052009 A052010
Sequence in context: A017913 A140428 A027154 this_sequence A117480 A018260 A023656
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KEYWORD
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nonn,nice,hard
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AUTHOR
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G. L. Honaker, Jr. (honak3r(AT)bvunet.net) and Patrick De Geest (pdg(AT)worldofnumbers.com), Nov 15 1999.
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EXTENSIONS
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11795 from Farideh Firoozbakht (f.firoozbakht(AT)sci.ui.ac.ir), Aug 21 2003
88071 from Hugo Pfoertner (hugo(AT)pfoertner.org), Dec 26 2004
More terms from Henri Lifchitz submitted by Ray Chandler (rayjchandler(AT)sbcglobal.net), Mar 02 2007
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