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Search: id:A083846
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| A083846 |
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a(n) is the largest prime of the form x^2 + 1 <= 10^n. |
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+0
6
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| 5, 37, 677, 8837, 98597, 972197, 9985601, 99800101, 999444997, 9999200017, 99986234437, 999920001601, 9999799764517, 99999200001601, 999999202999697, 9999993200001157, 99999979750774757, 999999848000005777
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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It is conjectured that this sequence is infinite, but this has never been proved. It is easily shown that all terms greater than 5 end in 1 or 7.
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REFERENCES
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G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 17.
P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 190.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. Landau's Problems.
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MATHEMATICA
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Do[ k = Floor[ Sqrt[ 10^n] - 1]; While[ !PrimeQ[k^2 + 1], k-- ]; Print[k^2 + 1], {n, 1, 19}]
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CROSSREFS
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Cf. A005574, A002496, A083844, A083845, A083847, A083848, A083849.
Sequence in context: A003709 A095957 A121834 this_sequence A003213 A090439 A089795
Adjacent sequences: A083843 A083844 A083845 this_sequence A083847 A083848 A083849
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KEYWORD
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nonn
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AUTHOR
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Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 05 2003
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), May 08 2003
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