cp's OEIS Frontend

A292676 Least number of symbols required to fill a grid of size n X n row by row in the greedy way such that in any row or column or rectangular 6 X 6 block no symbol occurs twice.

%I A292676 #10 Feb 16 2025 08:33:51
%S A292676 1,4,9,16,25,36,38,38,40,40,41,41,43,45,48,48,50,49,49,49,49,50,50,51,
%T A292676 51,52,51,52,53,53,53,53,53,53,55,53,55,55,59,59,59,61,65,64,66,70,68,
%U A292676 69,72,73,78,78,79,84,85,85,86,90,90,90,94,93,96,97,99,102,105,106,106,107
%N A292676 Least number of symbols required to fill a grid of size n X n row by row in the greedy way such that in any row or column or rectangular 6 X 6 block no symbol occurs twice.
%C A292676 Consider the symbols as positive integers. By the greedy way we mean to fill the grid row by row from left to right always with the least possible positive integer such that the three constraints (on rows, columns and rectangular blocks) are satisfied.
%C A292676 In contrast to the sudoku case, the 6 X 6 rectangles have "floating" borders, so the constraint is actually equivalent to say that an element must be different from all neighbors in a Moore neighborhood of range 5 (having up to 11*11 = 121 grid points).
%H A292676 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MooreNeighborhood.html">Moore Neighborhood</a>
%o A292676 (PARI) a(n,m=6,g=matrix(n,n))={my(ok(g,k,i,j,m)=if(m,ok(g[i,],k)&&ok(g[,j],k)&&ok(concat(Vec(g[max(1,i-m+1)..i,max(1,j-m+1)..min(#g,j+m-1)])),k),!setsearch(Set(g),k))); for(i=1,n,for(j=1,n,for(k=1,n^2,ok(g,k,i,j,m)&&(g[i,j]=k)&&break)));vecmax(g)} \\ without "vecmax" the program returns the full n X n board.
%o A292676 (Python) # uses function in A292673
%o A292676 print([A292673(n, b=6) for n in range(1, 101)]) # _Michael S. Branicky_, Apr 13 2023
%Y A292676 Cf. A292670, A292671, A292672, ..., A292679
%K A292676 nonn
%O A292676 1,2
%A A292676 _M. F. Hasler_, Sep 20 2017
%E A292676 Terms a(60) and beyond from _Andrew Howroyd_, Feb 22 2020