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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
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.)