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.
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, 7, 7, 9, 13, 12, 13, 16, 13, 12, 13, 16, 13, 12, 13, 16, 13, 12, 13, 16, 13, 12, 13, 16, 13, 12, 13, 16, 21, 19, 19, 21, 25, 21, 19, 19, 21, 25, 21, 19, 19
Offset: 0
Keywords
Links
- Rémy Sigrist, Table of n, a(n) for n = 0..10000
- Rémy Sigrist, PARI program for A345439
- N. J. A. Sloane, The start of the hexagonal spiral, showing the numbering of the cells. [An enlargement of Figure 1 of Wichmann (2019). The gray cells are the Eisenstein primes.]
- N. J. A. Sloane, Illustration of initial terms. [The cell numbers are black, their norms are red.]
- Brian Wichmann, Tiling for Unique Factorization Domains, Jul 22 2019.
- Brian Wichmann, The Eisenstein integers, with the primes shaded [Figure 1 from the previous link]
Programs
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PARI
See Links section.
Extensions
More terms from Rémy Sigrist, Jun 26 2021