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A035050
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a(n) = smallest k such that 2^n*k+1 is prime.
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14
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1, 1, 1, 2, 1, 3, 3, 2, 1, 15, 12, 6, 3, 5, 4, 2, 1, 6, 3, 11, 7, 11, 25, 20, 10, 5, 7, 15, 12, 6, 3, 35, 18, 9, 12, 6, 3, 15, 10, 5, 6, 3, 9, 9, 15, 35, 19, 27, 15, 14, 7, 14, 7, 20, 10, 5, 27, 29, 54, 27, 31, 36, 18, 9, 12, 6, 3, 9, 31, 23, 39, 39, 40, 20, 10, 5, 58, 29, 15, 36, 18, 9, 13
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Contribution from Ulrich Krug (leuchtfeuer37(AT)gmx.de), Jun 05 2010: (Start)
If a(i) = 2 * m then a(i+1) = m
Proof: (I) a(i) = 2*m, 2*m * 2^i + 1 = m*2^(i+1) + 1 prime, so a(i+1) <= m
(II) if a(i+1) = m-d for an integer d > 0, (m-d) * 2^(i+1) + 1 = (2*m-2*d) * 2^i + 1 prime
(2m-2d) < 2m contradiction to a(i) = 2 * m, d = 0
(End)
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
Index entries for sequences related to primes in arithmetic progressions
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EXAMPLE
| a(3)=2 because 1*2^3+1=9 is composite, 2*2^3+1=17 is prime.
a(99)=219 because 2^99k+1 is not prime for k=1,2,..,218. The first term which is not a composite number of this arithmetic progression is 2^99*219+1.
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MATHEMATICA
| a = {}; Do[k = 0; While[ ! PrimeQ[k 2^n + 1], k++ ]; AppendTo[a, k], {n, 0, 100}]; a (*Artur Jasinski*)
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CROSSREFS
| Analogous case is A034693. Special subscripts (n's for a(n)=1) are the exponents of known Fermat-primes: A000215. See also Fermat numbers A000051.
Cf. A007522, A127575, A127576, A127577, A127578, A127580, A127581, A087522, A127586.
Cf. A057778, A085427, A126717
Sequence in context: A071463 A047679 A179480 * A198790 A046819 A159945
Adjacent sequences: A035047 A035048 A035049 * A035051 A035052 A035053
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu)
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