

A083848


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


4



1, 1, 2, 2, 4, 6, 10, 14, 20, 26, 40, 56, 90, 126, 180, 250, 350, 496, 716, 1010, 1440, 2034, 2896, 4086, 5774, 8184, 11566, 16380, 23166, 32766, 46326, 65534, 92666, 131070, 185354, 262130, 370714, 524260, 741454, 1048554, 1482904, 2097146
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OFFSET

1,3


COMMENTS

It is conjectured that this sequence is infinite, but this has never been proved.
Ratio of successive terms appears to approach sqrt(2).  Bill McEachen, Nov 03 2013


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. SpringerVerlag, 1991, p. 190.


LINKS

Table of n, a(n) for n=1..42.
Eric Weisstein's World of Mathematics, Landau's Problems.


CROSSREFS

Cf. A005574, A002496, A083844, A083845, A083846, A083847, A083849.
Sequence in context: A034406 A098330 A240310 * A278297 A139582 A276059
Adjacent sequences: A083845 A083846 A083847 * A083849 A083850 A083851


KEYWORD

nonn


AUTHOR

Harry J. Smith, May 05 2003


STATUS

approved



