|
Search: id:A083845
|
|
|
| A083845 |
|
a(n)^2 + 1 is largest prime of the form x^2 + 1 <= 10^n. |
|
+0
6
|
|
| 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
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
It is conjectured that this sequence is infinite, but this has never been proved.
|
|
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.
|
|
MATHEMATICA
|
Do[ k = Floor[ Sqrt[ 10^n] - 1]; While[ !PrimeQ[k^2 + 1], k-- ]; Print[k], {n, 1, 25}]
|
|
CROSSREFS
|
Cf. A005574, A002496, A083844, A083846, A083847, A083848, A083849.
Sequence in context: A092438 A027207 A027231 this_sequence A027239 A050890 A114710
Adjacent sequences: A083842 A083843 A083844 this_sequence A083846 A083847 A083848
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 05 2003
|
|
EXTENSIONS
|
Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), May 08 2003
|
|
|
Search completed in 0.007 seconds
|
