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A082200 Triangle T(j,k) for 1 <= k <= j is filled row by row in the following manner: T(1,1) = 1; T(j,k) is the smallest nonprime number not yet used which is coprime to its left, left upper, upper and right upper neighbor, provided that such a neighbor exists (i.e., belongs to the triangle). Sequence contains the triangle by rows. 3

%I

%S 1,4,9,25,49,8,6,121,15,77,35,169,16,221,10,12,187,21,209,27,91,65,

%T 361,20,289,32,55,18,14,33,161,39,133,299,119,95,85,247,34,125,22,45,

%U 44,69,26,24,203,81,217,323,259,377,155,287,51,115,143,38,145,36,205,46,57,52

%N Triangle T(j,k) for 1 <= k <= j is filled row by row in the following manner: T(1,1) = 1; T(j,k) is the smallest nonprime number not yet used which is coprime to its left, left upper, upper and right upper neighbor, provided that such a neighbor exists (i.e., belongs to the triangle). Sequence contains the triangle by rows.

%C This results in a triangle, where each element is coprime to all of its (at most eight) neighbors.

%C A rearrangement of nonprimes.

%e The first few rows of the triangle are

%e 1;

%e 4, 9;

%e 25, 49, 8;

%e 6, 121, 15, 77;

%e 35, 169, 16, 221, 10;

%e 12, 187, 21, 209, 27, 91;

%e T(4,2) = 121 is coprime to its neighbors 25, 49, 8, 6, 15, 35, 169 and 16.

%o (PARI) {unused(m,T,j,k)=b=1; for(jj=1,j-1, for(kk=1,jj,if(T[jj,kk]==m,b=0))); for(kk=1,k-1,if(T[j,kk]==m,b=0)); b}

%o (PARI) {nextnum(T,j,k)=t=1; m=4; while(t>0,if(!isprime(m)&&unused(m,T,j,k)&&if(k>1,gcd(m,T[j-1,k-1])==1,1)&&if(k<j,gcd(m,T[j-1,k]),1)==1&&if(k<j-1,gcd(m,T[j-1,k+1])==1,1)&&if(k>1,gcd(m,T[j,k-1])==1,1),t=0,m++)); m}

%o (PARI) {n=50; T=matrix(n,n); T[1,1]=1; for(j=2,n, for(k=1,j,print1(T[j,k]=nextnum(T,j,k),","))); for(j=1,n, for(k=1,j,print1(T[j,k],",")))}

%Y Cf. A082201, A082202, A082203.

%K nonn,tabl

%O 1,2

%A _Amarnath Murthy_, Apr 07 2003

%E Edited, corrected and extended by _Klaus Brockhaus_, May 14 2003

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Last modified August 11 18:37 EDT 2020. Contains 336428 sequences. (Running on oeis4.)