|
| |
|
|
A222596
|
|
Length of the closed curve through Gaussian primes described in A222594.
|
|
2
|
|
|
|
6, 64, 64, 8, 32, 92, 92, 32, 8, 32, 12, 92, 32, 12, 48, 412, 12, 412, 48, 48, 92, 92, 44, 92, 92, 12, 1316, 48, 44, 412, 48, 48, 412, 412, 24, 44, 24, 48, 1316, 12, 8, 48, 1316, 412, 44, 1316, 1316, 12, 12, 1316, 1316, 1316, 412, 44, 412, 204, 1316, 28, 72, 412
(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 A222594 and A222595 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
|
T. D. Noe, Table of n, a(n) for n = 1..2829
|
|
|
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]]; nn = 20; ps = {}; Do[If[PrimeQ[i + (j - i) I, GaussianIntegers -> True], AppendTo[ps, i + (j-i)*I]], {j, 0, nn}, {i, 0, j}]; Table[loop[ps[[n]]]; Total[Abs[Differences[lst]]], {n, Length[ps]}]
|
|
|
CROSSREFS
|
Cf. A222298 (spiral lengths beginning at the n-th positive real Gaussian prime).
Sequence in context: A249590 A034665 A218383 * A067447 A083225 A320528
Adjacent sequences: A222593 A222594 A222595 * A222597 A222598 A222599
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
T. D. Noe, Feb 27 2013
|
|
|
STATUS
|
approved
|
| |
|
|
