|
|
A222300
|
|
Length of the closed curve through Gaussian primes described in A222298.
|
|
3
|
|
|
32, 48, 1316, 72, 1536, 168, 168, 152, 152, 1536, 140, 352, 352, 132, 172, 280, 648, 132, 92, 12, 96, 32, 332, 332, 460, 30492, 652, 328, 460, 30492, 748, 236, 64, 112, 204, 336, 336, 24560, 24560, 448, 440, 13016, 1536, 316, 108, 2224, 132, 116, 864, 80, 1128
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The Gaussian prime spiral is described in the short note by O'Rourke and Wagon. It is not known if every iteration is a closed loop. See A222298 for the number of line segments between primes.
|
|
REFERENCES
|
Joseph O'Rourke and Stan Wagon, Gaussian prime spirals, Mathematics Magazine, vol. 86, no. 1 (2013), p. 14.
|
|
LINKS
|
|
|
EXAMPLE
|
The loop beginning with 31 is {31, 43, 43 - 8i, 37 - 8i, 37 - 2i, 45 - 2i, 45 - 8i, 43 - 8i, 43, 47, 47 - 2i, 45 - 2i, 45 + 2i, 47 + 2i, 47, 43, 43 + 8i, 45 + 8i, 45 + 2i, 37 + 2i, 37 + 8i, 43 + 8i, 43, 31}. This loop is 168 units long.
|
|
MATHEMATICA
|
loop[n_] := Module[{p = n, direction = 1}, lst = {n}; While[While[p = p + direction; ! PrimeQ[p, GaussianIntegers -> True]]; direction = direction*(-I); AppendTo[lst, p]; ! (p == n && direction == 1)]; Length[lst]]; cp = Select[Range[1000], PrimeQ[#, GaussianIntegers -> True] &]; Table[loop[p]; Total[Abs[Differences[lst]]], {p, cp}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|