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Search: id:A083849
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| A083849 |
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a(n) is the largest prime of the form x^2 + 1 <= 2^n. |
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+0
6
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| 2, 2, 5, 5, 17, 37, 101, 197, 401, 677, 1601, 3137, 8101, 15877, 32401, 62501, 122501, 246017, 512657, 1020101, 2073601, 4137157, 8386817, 16695397, 33339077, 66977857, 133772357, 268304401, 536663557, 1073610757, 2146098277
(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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CROSSREFS
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Cf. A005574, A002496, A083844, A083845, A083846, A083847, A083848.
Sequence in context: A056470 A056471 A164904 this_sequence A063501 A103892 A000403
Adjacent sequences: A083846 A083847 A083848 this_sequence A083850 A083851 A083852
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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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