cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A301639 a(n) = square of the distance from n to nearest cube of a Gaussian integer.

This page as a plain text file.
%I A301639 #14 Mar 28 2018 05:18:56
%S A301639 0,0,1,4,8,9,4,1,0,1,4,4,5,8,13,20,29,40,53,64,49,36,25,16,9,4,1,0,1,
%T A301639 4,9,16,25,36,49,64,81,100,121,130,117,106,97,90,85,82,81,82,85,90,97,
%U A301639 106,117,121,100,81,64,49,36,25,16,9,4,1,0,1,4,9,16,25
%N A301639 a(n) = square of the distance from n to nearest cube of a Gaussian integer.
%C A301639 The distance between two Gaussian integers is not necessarily integer, hence the use of the square of the distance.
%C A301639 This sequence is a variant of A074989: here we minimize norm(n - z^3) where z runs through every Gaussian integers, there we minimize abs(n - m^3) where m runs through every integers.
%H A301639 Rémy Sigrist, <a href="/A301639/b301639.txt">Table of n, a(n) for n = 0..10000</a>
%H A301639 Rémy Sigrist, <a href="/A301639/a301639.png">Scatterplot of this sequence versus A074989^2 for n = 0..1000</a>
%H A301639 Wikipedia, <a href="https://en.wikipedia.org/wiki/Gaussian_integer">Gaussian integer</a>
%H A301639 <a href="/index/Di#distance_to_the_nearest">Index entries for sequences related to distance to nearest element of some set</a>
%F A301639 a(n) = A301626(n, 0).
%F A301639 a(n) <= A074989(n)^2.
%e A301639 For n = 4: the nearest Gaussian cubes to 4 are 2 + 2*i and 2 - 2*i, hence a(4) = (4-2)^2 + 2^2 = 8.
%Y A301639 Cf. A074989, A301626.
%K A301639 nonn
%O A301639 0,4
%A A301639 _Rémy Sigrist_, Mar 25 2018