A211340 -id:A211340 - cp's OEIS frontend

A228234 Number of strict Gaussian primes of norm less than or equal to n in the first quadrant on or below the first diagonal.

0, 1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 16, 18, 21, 22, 25, 29, 32, 35, 38, 42, 45, 47, 50, 55, 59, 62, 67, 71, 75, 79, 84, 88, 94, 99, 104, 108, 113, 117, 120, 127, 134, 137, 144, 149, 155, 160, 168, 176, 181, 185, 193, 202, 208, 213, 220, 227, 233, 241, 248, 256

Offset: 1

Olivier Gérard, Aug 17 2013

nonn

Strict means that one does not include the ordinary integer primes and integer primes multiplied by i.

In the first quadrant and on or below the first diagonal, means here that the imaginary part is positive and inferior or equal to the real part.

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A211340 (number of strict Gaussian integers in this half-quadrant).
Cf. A228235 (a version of this sequence including the real axis).
Cf. A228232, A228233 (versions counting the whole first quadrant).

nn = 100; t = Select[Flatten[Table[a + b*I, {a, 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 *)

A228172 Number of integer pairs (x,y) such that 0<=y<=x, x>0, and x^2+y^2<=n^2.

Original entry on oeis.org

1, 3, 6, 9, 14, 19, 24, 31, 39, 48, 56, 65, 77, 88, 101, 113, 127, 141, 157, 174, 189, 208, 226, 244, 266, 287, 309, 330, 353, 378, 401, 428, 454, 482, 511, 537, 568, 596, 630, 662, 692, 726, 760, 797, 833, 867, 905, 942, 982, 1023, 1065, 1106, 1146, 1189, 1231, 1278, 1322, 1369, 1414, 1462, 1512

Offset: 1

Olivier Gérard, Aug 17 2013

nonn

This corresponds to points of positive norm less than or equal to n on the square lattice, in the first quadrant, on or below the first diagonal.

Cf. A211340 (version excluding the cases with y=0).

a(n) = A211340 (n) + n . [Joerg Arndt, Aug 19 2013]

cp's OEIS Frontend

A228234 Number of strict Gaussian primes of norm less than or equal to n in the first quadrant on or below the first diagonal.

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