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.

1, 4, 9, 25, 49, 8, 6, 121, 15, 77, 35, 169, 16, 221, 10, 12, 187, 21, 209, 27, 91, 65, 361, 20, 289, 32, 55, 18, 14, 33, 161, 39, 133, 299, 119, 95, 85, 247, 34, 125, 22, 45, 44, 69, 26, 24, 203, 81, 217, 323, 259, 377, 155, 287, 51, 115, 143, 38, 145, 36, 205, 46, 57, 52

Offset

1,2

Comments

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

A rearrangement of nonprimes.

Links

Table of n, a(n) for n=1..64.

Example

The first few rows of the triangle are
   1;
   4,   9;
  25,  49,   8;
   6, 121,  15,  77;
  35, 169,  16, 221,  10;
  12, 187,  21, 209,  27,  91;
T(4,2) = 121 is coprime to its neighbors 25, 49, 8, 6, 15, 35, 169 and 16.

Prog

(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}
(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}
(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], ", ")))}

Crossrefs

Cf. A082201, A082202, A082203.

Sequence in context: A350322 A158142 A158143 * A244557 A063482 A277312

Adjacent sequences: A082197 A082198 A082199 * A082201 A082202 A082203

Keyword

nonn,tabl

Author

Amarnath Murthy, Apr 07 2003

Extensions

Edited, corrected and extended by Klaus Brockhaus, May 14 2003

Status

approved