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Search: id:A134876
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| A134876 |
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Number of Proth primes; primes of the form 1 + k*2^n with k odd and k < 2^n. |
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+0
2
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| 1, 2, 1, 3, 4, 8, 18, 23, 44, 73, 142, 277, 484, 871, 1644, 3060, 5851, 10917, 20776, 39263, 74752, 142521, 271223, 520242, 996486, 1916486, 3686628, 7103236, 13702428, 26469008
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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All primes were found by Mathematica's PrimeQ function and proved using Proth's theorem. The ratio of consecutive terms is about 1.93.
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LINKS
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Eric Weisstein's World of Mathematics, MathWorld: Proth's Theorem
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EXAMPLE
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a(1)=1 because 3 is the only Proth prime for n=1. a(2)=2 because 5 and 13 are the only primes for n=2. a(3)=1 because 41 is the only prime for n=3.
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MATHEMATICA
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Table[cnt=0; Do[If[PrimeQ[1+k*2^n], cnt++ ], {k, 1, 2^n, 2}]; cnt, {n, 20}]]
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CROSSREFS
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Cf. A080076.
Sequence in context: A000032 A061084 A055391 this_sequence A019612 A007444 A166476
Adjacent sequences: A134873 A134874 A134875 this_sequence A134877 A134878 A134879
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Nov 17 2007
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