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

0,8

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]

Prog

(PARI) See Links section.

Crossrefs

Cf. A336336, A345435.

Sequence in context: A102745 A108026 A010702 * A095925 A242744 A066783

Adjacent sequences: A345436 A345437 A345438 * A345440 A345441 A345442

Keyword

nonn

Author

N. J. A. Sloane, Jun 25 2021

Extensions

More terms from Rémy Sigrist, Jun 26 2021

Status

approved