

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



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
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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, j1, for(kk=1, jj, if(T[jj, kk]==m, b=0))); for(kk=1, k1, 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[j1, k1])==1, 1)&&if(k<j, gcd(m, T[j1, k]), 1)==1&&if(k<j1, gcd(m, T[j1, k+1])==1, 1)&&if(k>1, gcd(m, T[j, k1])==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: A046451 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



