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
AUTHOR
Nathaniel J. Strout, Dec 04 2019
STATUS
approved