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A083849 a(n) is the largest prime of the form x^2 + 1 <= 2^n. +0
6
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)
OFFSET

1,1

COMMENT

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.

REFERENCES

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.

LINKS

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. Landau's Problems.

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 05 2003

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Last modified November 24 23:16 EST 2009. Contains 167481 sequences.


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