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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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3
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2, 1, 1, 2, 1, 7954, 1, 34, 101, 2, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 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 (mymontain(AT)yahoo.com), 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
| a[n_]:=(For[m=1, !PrimeQ[n^m+m], m++ ]; m)
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EXAMPLE
| a(3)=2 because 3^2+2 is prime and 3^1+1 is composite.
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MATHEMATICA
| a[n_]:=(For[m=1, !PrimeQ[n^m+m], m++ ]; m); Do[Print[a[n]], {n, 0, 10}]
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CROSSREFS
| Sequence in context: A126127 A060256 A103899 * A169676 A034798 A171531
Adjacent sequences: A093321 A093322 A093323 * A093325 A093326 A093327
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KEYWORD
| more,nonn
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AUTHOR
| Farideh Firoozbakht (mymontain(AT)yahoo.com), May 11 2004
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EXTENSIONS
| a(11) is greater than 8651. - Robert G. Wilson v May 24 2004
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