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A345440
Represent the ring R = {x+y*sqrt(-2): x, y rational integers} by the cells centered at the points (x,y) of a square grid, as in A345437; number the cells of the grid along a counterclockwise square spiral, with the cells at (0,0) and (1,0) numbered 0, 1; then a(n) is the norm x^2+2*y^2 of the element of R occupying the n-th cell.
1
0, 1, 3, 2, 3, 1, 3, 2, 3, 6, 4, 6, 12, 9, 8, 9, 12, 6, 4, 6, 12, 9, 8, 9, 12, 17, 11, 9, 11, 17, 27, 22, 19, 18, 19, 22, 27, 17, 11, 9, 11, 17, 27, 22, 19, 18, 19, 22, 27, 34, 24, 18, 16, 18, 24, 34, 48, 41, 36, 33, 32, 33, 36, 41, 48, 34, 24, 18, 16, 18, 24
OFFSET
0,3
LINKS
N. J. A. Sloane, Illustration of initial terms [An enlargement of Figure 3 of Wichmann (2019), showing the numbering of the initial cells of the square spiral. The origin is black, the two units +-1 are red, and the primes are blue.]
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.
FORMULA
a(n) = A174344(n+1)^2 + 2*A274923(n+1)^2. - Rémy Sigrist, Jun 26 2021
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 25 2021
EXTENSIONS
More terms from Rémy Sigrist, Jun 26 2021
STATUS
approved