|
Search: id:A068785
|
|
|
| A068785 |
|
Number of Cartesian lattice points in or on the circle of radius 10^n. |
|
+0
5
|
|
| 1, 37, 317, 3149, 31417, 314197, 3141549, 31416025, 314159053
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
a(n) ~ pi*n. page 164. "Gauss gave a(100) = 317 and a(10,000) = 31417." page 165. a(10^8) = 314159053, a(10^10) = 31415925457, a(10^12) = 3141592649625 & a(10^14) = 314159265350589. page 234.
|
|
REFERENCES
|
Daniel Shanks, "Solved and Unsolved Problems in Number Theory," Fourth Edition, Chelsea Publishing Co., NY, 1993, pages 165 and 234.
Wolfram Research, Mathematica 4, Standard Add-On Packages, Wolfram Media, Inc., Champaign, Il, 1999, pages 322-3.
|
|
LINKS
|
Index entries for sequences related to populations of quadratic forms
|
|
MATHEMATICA
|
Needs["NumberTheory`NumberTheoryFunctions`"]; k = 1; s = 1; Do[s = s + SumOfSquaresR[2, n]; If[n == 10^k, k++; Print[s]], {n, 1, 10^6} ]
|
|
CROSSREFS
|
Cf. A004018, A057961, A057655.
Sequence in context: A114785 A061014 A130450 this_sequence A133554 A137834 A124337
Adjacent sequences: A068782 A068783 A068784 this_sequence A068786 A068787 A068788
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 07 2002
|
|
|
Search completed in 0.002 seconds
|
