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Search: id:A093324
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| A093324 |
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a(n) is the smallest natural number m such that n^m+m is prime. |
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4
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| 2, 1, 1, 2, 1, 7954, 1, 34, 101, 2, 1
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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a(n)=1 iff n+1 is prime. For n>1 n+a(n) is odd (for n>1 a(n) is odd iff n is even). a(11) is greater than 7000. a(m) for m=12,13,14,15,16,17 and 18 are:1,54,17,2,1,1080,1. 5^7954+7954 is a 5560-digit probable prime.
a(11) is greater than 20165, so every prime of the form 11^m+m has more than 21000 digits. - Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Jun 10 2004
a(11) is greater than 80000. - T. D. Noe (noe(AT)sspectra.com), Mar 07 2007
a(11) is greater than 190000. [From T. D. Noe (noe(AT)sspectra.com), Jul 31 2008]
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FORMULA
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a[n_]:=(For[m=1, !PrimeQ[n^m+m], m++ ]; m)
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EXAMPLE
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a(3)=2 because 3^2+2 is prime and 3^1+1 is composite.
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MATHEMATICA
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a[n_]:=(For[m=1, !PrimeQ[n^m+m], m++ ]; m); Do[Print[a[n]], {n, 0, 10}]
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CROSSREFS
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Sequence in context: A126127 A102578 A103899 this_sequence A034798 A115236 A064286
Adjacent sequences: A093321 A093322 A093323 this_sequence A093325 A093326 A093327
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KEYWORD
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more,nonn,new
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AUTHOR
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Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), May 11 2004
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EXTENSIONS
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a(11) is greater than 8651. - Robert G. Wilson v May 24 2004
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