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Search: id:A083847
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| A083847 |
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a(n) = number of primes of the form x^2 + 1 <= 2^n. |
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+0
6
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| 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 14, 18, 24, 33, 42, 54, 70, 91, 114, 158, 212, 293, 393, 539, 713, 957, 1301, 1792, 2459, 3378, 4615, 6233, 8418, 11540, 15867, 21729, 29843, 41169, 56534, 77697, 106787, 147067, 203025, 280340, 387308, 535153, 739671, 1023655, 1416635, 1960813, 2716922, 3764693, 5218926, 7238715
(list; graph; listen)
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OFFSET
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1,3
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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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C. K. Caldwell, AN AMAZING PRIME HEURISTIC A pdf file.
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, A083848, A083849.
Sequence in context: A034141 A055002 A114097 this_sequence A034142 A008675 A027581
Adjacent sequences: A083844 A083845 A083846 this_sequence A083848 A083849 A083850
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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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More terms from Alex Healy, Feb 06 2005
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