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A083845
a(n)^2 + 1 is largest prime of the form x^2 + 1 <= 10^n.
5
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
OFFSET
1,1
COMMENTS
It is conjectured that the number of primes of the form x^2+1 is infinite and thus this sequence never becomes a constant, but this has not been proved.
The ratio a(n+2)/a(n) appears to approach 10, as one might expect. - 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. Springer-Verlag, 1991, p. 190.
LINKS
Eric Weisstein's World of Mathematics, Landau's Problems.
MATHEMATICA
Do[ k = Floor[ Sqrt[ 10^n] - 1]; While[ !PrimeQ[k^2 + 1], k-- ]; Print[k], {n, 1, 25}]
KEYWORD
nonn
AUTHOR
Harry J. Smith, May 05 2003
EXTENSIONS
Edited and extended by Robert G. Wilson v, May 08 2003
STATUS
approved