A066643 -id:A066643 - cp's OEIS frontend

A338020 a(n) is the number of circles of positive integer area with radii less than n and greater than n - 1.

3, 9, 16, 22, 28, 35, 40, 48, 53, 60, 66, 72, 78, 85, 91, 98, 103, 110, 117, 122, 129, 135, 141, 148, 154, 160, 167, 173, 179, 185, 192, 197, 205, 210, 217, 223, 229, 236, 242, 248, 255, 260, 267, 274, 279, 286, 292, 299, 304, 311, 318, 323, 330, 336, 343, 349, 355, 361, 367

Offset: 1

Torlach Rush, Oct 06 2020

nonn

Conjecture: k >= 2, each triple Tr(k) = {a(k), a(k+1), a(k+2)} gives the sides of an integer-sided triangle, and {(a(k+2) - a(k)), (a(k+2) - a(k+1)), (a(k+1) - a(k))} is a degenerate integer-sided triangle.

Cf. A066643 (partial sums).

ap(n) = {my(x = 0, y = 1, ia = 1); while(y, if(n > sqrt(ia / Pi), x++; ia++, y = 0)); return(x)}
a(n) = {my(x = 0, y = 1, ia = 1); while(y, if(n > sqrt(ia / Pi), x++; ia++, y = 0)); return(x - ap(n-1))}
for(i = 1, 70, print1(a(i), ", "))

a(n) = #{floor(sqrt(k/Pi)) < n: n > 0, k > 0}.

a(n) = A066643(n)-A066643(n-1). - R. J. Mathar, Jan 25 2023

A235532 a(n) = floor(n^2 * (4-Pi)).

Original entry on oeis.org

0, 0, 3, 7, 13, 21, 30, 42, 54, 69, 85, 103, 123, 145, 168, 193, 219, 248, 278, 309, 343, 378, 415, 454, 494, 536, 580, 625, 672, 721, 772, 824, 879, 934, 992, 1051, 1112, 1175, 1239, 1305, 1373, 1442, 1514, 1587, 1661, 1738, 1816, 1896, 1977, 2061, 2146, 2232, 2321

Offset: 0

Alex Ratushnyak, Jan 11 2014

nonn

a(n) = floor(As(n) - Ac(n)), where Ac(n) is the area of the circle of radius n, and As(n) is the area of square with side length 2n.

Cf. A066643, A057672, A000290.

Floor[(4-Pi)#^2]&/@Range[0,60] (* Harvey P. Dale, Jan 10 2020 *)

import math
for n in range(77): print(str(int(n*n*(4-math.pi))), end=',')

cp's OEIS Frontend

A338020 a(n) is the number of circles of positive integer area with radii less than n and greater than n - 1.

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