|
|
A228235
|
|
Number of Gaussian primes of norm less than or equal to n in the first quadrant on or below the first diagonal.
|
|
2
|
|
|
0, 1, 3, 4, 5, 6, 9, 11, 12, 14, 18, 19, 21, 24, 25, 28, 32, 35, 39, 42, 46, 49, 52, 55, 60, 64, 67, 72, 76, 80, 85, 90, 94, 100, 105, 110, 114, 119, 123, 126, 133, 140, 144, 151, 156, 162, 168, 176, 184, 189, 193, 201, 210, 216, 221, 228, 235, 241, 250, 257
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
In the first quadrant and on or below the first diagonal, means here that the imaginary part is nonnegative and inferior or equal to the real part.
The norm used is the absolute value of the Gaussian integers, seen as complex numbers : sqrt( re(z)^2 + im(z)^2).
|
|
LINKS
|
|
|
MATHEMATICA
|
nn = 100; t = Select[Flatten[Table[a + b*I, {a, 0, nn}, {b, a, nn}]], PrimeQ[#, GaussianIntegers -> True] &]; t2 = Table[0, {nn}]; Do[f = Ceiling[Abs[i]]; If[f <= nn, t2[[f]]++], {i, t}]; Accumulate[t2] (* T. D. Noe, Aug 19 2013 *)
|
|
CROSSREFS
|
Cf. A228172 (number of Gaussian integers in this half-quadrant).
Cf. A228234 (version of this sequence excluding the real axis).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|