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Search: id:A083845
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| A083845 |
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a(n)^2 + 1 is largest prime of the form x^2 + 1 <= 10^n. |
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+0
6
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| 2, 6, 26, 94, 314, 986, 3160, 9990, 31614, 99996, 316206, 999960, 3162246, 9999960, 31622764, 99999966, 316227734, 999999924, 3162277654, 9999999956, 31622776500, 99999999964, 316227766006, 999999999886, 3162277660140
(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.
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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], {n, 1, 25}]
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CROSSREFS
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Cf. A005574, A002496, A083844, A083846, A083847, A083848, A083849.
Sequence in context: A092438 A027207 A027231 this_sequence A027239 A050890 A114710
Adjacent sequences: A083842 A083843 A083844 this_sequence A083846 A083847 A083848
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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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