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 A279049 A 3-dimensional variant of A269526 "Infinite Sudoku": expansion (read first by layer, then by row) of square pyramid P(n,j,k). (See A269526 and "Comments" below for definition). 2
 1, 2, 3, 4, 5, 6, 1, 2, 7, 8, 4, 3, 2, 7, 3, 5, 6, 7, 9, 10, 3, 1, 1, 6, 5, 2, 5, 4, 1, 6, 4, 7, 8, 5, 6, 2, 11, 9, 10, 3, 12, 8, 13, 4, 5, 3, 2, 10, 7, 1, 8, 6, 11, 3, 2, 8, 10, 1, 4, 7, 5, 6, 3, 2, 11, 9, 8, 4, 1, 12, 8, 13, 6, 7, 5, 14, 9, 11, 3, 1, 4, 15, 5, 6, 7, 2, 7, 8, 1, 10, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Comments: Construct a square pyramid so the top left corners of each layer are directly underneath each other. Place a "1" in the top layer (P(1,1,1) = 1); in each successive layer starting in the top left corner (P(n,1,1)) and continuing horizontally until each successive row is complete: add the least positive integer so that no row, column or diagonal (in any horizontal or vertical direction) contains a repeated term. Here, the following definitions apply: "row" means a horizontal line (read left to right) on a layer; "horizontal column" means a line on a layer read vertically (downward) WITHIN a layer; "vertical column" means a vertical line (read downward) ACROSS layers; and "diagonal" means a diagonal line with slope 1 or -1 in any possible plane. Conjecture: all infinite lines (i.e., all vertical columns and some multi-layer diagonals) are permutations of the natural numbers (while this has been proven for rows and columns in A269526, proofs here will require more subtle analysis). LINKS EXAMPLE Example: Layers start P(1,1,1): Layer 1:          1                   ----- Layer 2:          2  3                   4  5                   -------- Layer 3:          6  1  2                   7  8  4                   3  2  7                   ----------- Layer 4:          3  5  6  7                   9 10  3  1                   1  6  5  2                   5  4  1  6                   ----------- Layer 4, Row 2, Column 1 = P(4,2,1) = 9. P(4,3,3) = 5 because all coefficients < 5 have appeared in at least one row, column or diagonal to P(4,3,3): P(4,2,4) and P(4,3,1) = 1; P(2,1,1) and P(3,3,2) = 2; P(4,1,1) and P(4,2,3) = 3; and P(3,2,3) = 4. Expanding successive layers (read by rows): 1 2, 3, 4, 5 6, 1, 2, 7, 8, 4, 3, 2, 7 3, 5, 6, 7, 9, 10, 3, 1, 1, 6, 5, 2, 5, 4, 1, 6 4, 7, 8, 5, 6, 2, 11, 9, 10, 3, 12, 8, 13, 4, 5, 3, 2, 10, 7, 1, 8, 6, 11, 3, 2 CROSSREFS Cf. A269526. Cf. A000330 (square pyramidal numbers). Sequence in context: A053828 A033927 A104414 * A125934 A125935 A327241 Adjacent sequences:  A279046 A279047 A279048 * A279050 A279051 A279052 KEYWORD nonn,tabf AUTHOR Bob Selcoe, Dec 04 2016 STATUS approved

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Last modified October 21 21:46 EDT 2019. Contains 328315 sequences. (Running on oeis4.)