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Search: id:A123252
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| A123252 |
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a(n) = smallest prime of the form 2^k + 2n - 1, k = 0, 1, ... |
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+0
2
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| 3, 5, 7, 11, 11, 13, 17, 17, 19, 23, 23, 31, 29, 29, 31, 47, 37, 37, 41, 41, 43, 47, 47, 79, 53, 53, 61, 59, 59, 61, 317, 67, 67, 71, 71, 73, 89, 79, 79, 83, 83, 211, 89, 89, 97, 107, 97, 97, 101, 101, 103, 107, 107, 109, 113, 113, 241, 131, 149, 127, 137, 127, 127, 131
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If n == 0 (mod 3) then the exponent k must be odd, if n>1 and n == 1 (mod 3) then k must be even and if n == 2 (mod 3) then k can be either.
Records: 3, 5, 7, 11, 13, 17, 19, 23, 31, 47, 79, 317, 1163, 1048847, 536871199, 2^955+773, ..., . Robert G. Wilson v.
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EXAMPLE
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For n = 4, p = 2 -> 2^2+(2*4-1) = 11, the fourth entry because 2^1+(2*4-1) which equals 9 is not a prime.
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MATHEMATICA
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f[n_] := Block[{p = 1}, While[ !PrimeQ[2^p + 2n - 1], p++ ]; 2^p + 2n - 1]; Array[f, 64] (* Robert G. Wilson v *)
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PROGRAM
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(PARI) g2(n) = forstep(k=1, n, 2, for(p=1, n, y=k+2^p; if(isprime(y), print1(y", "); break)))
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CROSSREFS
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Adjacent sequences: A123249 A123250 A123251 this_sequence A123253 A123254 A123255
Sequence in context: A022457 A066066 A112070 this_sequence A066168 A109908 A102941
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Oct 08 2006
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(at)rgwv.com), Nov 11 2006
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