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, 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

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