cp's OEIS Frontend

A345439 Consider the Eisenstein integers x + y*omega, x and y rational integers, represented as the cells of an hexagonal grid; draw a hexagonal spiral as in A345435; a(n) is the norm x^2-x*y+y^2 of the Eisenstein integer in the n-th cell of the spiral.

%I A345439 #20 Jun 26 2021 06:36:34
%S A345439 0,1,1,1,1,1,1,3,4,3,4,3,4,3,4,3,4,3,4,7,7,9,7,7,9,7,7,9,7,7,9,7,7,9,
%T A345439 7,7,9,13,12,13,16,13,12,13,16,13,12,13,16,13,12,13,16,13,12,13,16,13,
%U A345439 12,13,16,21,19,19,21,25,21,19,19,21,25,21,19,19
%N A345439 Consider the Eisenstein integers x + y*omega, x and y rational integers, represented as the cells of an hexagonal grid; draw a hexagonal spiral as in A345435; a(n) is the norm x^2-x*y+y^2 of the Eisenstein integer in the n-th cell of the spiral.
%H A345439 Rémy Sigrist, <a href="/A345439/b345439.txt">Table of n, a(n) for n = 0..10000</a>
%H A345439 Rémy Sigrist, <a href="/A345439/a345439.gp.txt">PARI program for A345439</a>
%H A345439 N. J. A. Sloane, <a href="/A345435/a345435.pdf">The start of the hexagonal spiral, showing the numbering of the cells.</a> [An enlargement of Figure 1 of Wichmann (2019). The gray cells are the Eisenstein primes.]
%H A345439 N. J. A. Sloane, <a href="/A345439/a345439.pdf">Illustration of initial terms.</a> [The cell numbers are black, their norms are red.]
%H A345439 Brian Wichmann, <a href="http://www.tilingsearch.org/special/ufd.pdf">Tiling for Unique Factorization Domains</a>, Jul 22 2019.
%H A345439 Brian Wichmann, <a href="/A345435/a345435.png">The Eisenstein integers, with the primes shaded</a> [Figure 1 from the previous link]
%o A345439 (PARI) See Links section.
%Y A345439 Cf. A336336, A345435.
%K A345439 nonn
%O A345439 0,8
%A A345439 _N. J. A. Sloane_, Jun 25 2021
%E A345439 More terms from _Rémy Sigrist_, Jun 26 2021