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 A330190 Symmetric matrix read by antidiagonals: f(i,j) = 1 + gcd(f(i-1,j), f(i,j-1)), where f(1,j) and f(i,1) are 1. 1
 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 3, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 3, 3, 3, 2, 1, 1, 2, 2, 4, 4, 2, 2, 1, 1, 2, 3, 3, 5, 3, 3, 2, 1, 1, 2, 2, 4, 2, 2, 4, 2, 2, 1, 1, 2, 3, 3, 3, 3, 3, 3, 3, 2, 1, 1, 2, 2, 4, 4, 4, 4, 4, 4, 2, 2, 1, 1, 2, 3, 3, 5, 5, 5, 5, 5, 3, 3, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS This matrix when displayed in a gray scale, from least to greatest, forms spikes of increasing numbers because large sections of the antidiagonals are the same number. See examples section. LINKS Michael De Vlieger, Table of n, a(n) for n = 1..11325 (Rows n = 1..150, flattened) Nathaniel J. Strout, 1000 X 1000 grid Michael De Vlieger, 2048 X 2048 grid with color function where black = 1, red = 2 and magenta represents the maximum value in the grid (i.e., f(312,768) = f(768,312) = 41). EXAMPLE An example of a triangle described in the comment: ........... ........... ..........2 ........2 3 ......2 3 4 ....2 3 4 5 Array begins: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, ... 1, 2, 3, 2, 3, 2, 3, 2, 3, 2, ... 1, 2, 2, 3, 4, 3, 4, 3, 4, 3, ... 1, 2, 3, 4, 5, 2, 3, 4, 5, 2, ... 1, 2, 2, 3, 2, 3, 4, 5, 6, 3, ... 1, 2, 3, 4, 3, 4, 5, 6, 7, 2, ... 1, 2, 2, 3, 4, 5, 6, 7, 8, 3, ... 1, 2, 3, 4, 5, 6, 7, 8, 9, 4, ... 1, 2, 2, 3, 2, 3, 2, 3, 4, 5, ... ... MATHEMATICA f[1, j_] := f[1, j] = 1; f[i_, 1] := f[i, 1] = 1; f[i_, j_] := f[i, j] = 1 + GCD[f[i - 1, j], f[i, j - 1]]; Table[f[m - k + 1, k], {m, 13}, {k, m, 1, -1}] // Flatten (* Michael De Vlieger, Aug 03 2022 *) PROG (PARI) T(n)={my(M=matrix(n, n, i, j, 1)); for(i=2, n, for(j=2, n, M[i, j] = 1 + gcd(M[i-1, j], M[i, j-1]))); M} { my(A=T(10)); for(i=1, #A, print(A[i, ])) } \\ Andrew Howroyd, Jan 25 2020 CROSSREFS Sequence in context: A245851 A230596 A307079 * A356300 A348041 A003983 Adjacent sequences: A330187 A330188 A330189 * A330191 A330192 A330193 KEYWORD nonn,tabl,look AUTHOR Nathaniel J. Strout, Dec 04 2019 STATUS approved

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Last modified July 16 08:10 EDT 2024. Contains 374345 sequences. (Running on oeis4.)