A081485 - OEIS

%I #8 Dec 05 2013 19:56:01

%S 1,1,3,1,2,3,1,3,5,7,1,2,3,5,19,1,3,5,7,13,19,1,2,3,5,7,11,13,1,3,5,7,

%T 11,13,17,23,1,2,3,5,7,11,13,17,31,1,3,5,7,11,13,17,19,23,31,1,2,3,5,

%U 7,11,13,17,19,23,31,1,3,5,7,11,13,17,19,23,29,41,47,1,2,3,5,7,11,13,17

%N Triangle read by rows in which the n-th row contains the smallest set of n coprime numbers with a sum which is a multiple of n.

%C In the row for 6 the fifth term is 13 and not 11 as this forces the sixth term divisible by (not coprime to 3) 3. For even n all the terms have to be odd. This sequence set should exhibit some interesting properties and needs attention.

%H Franklin T. Adams-Watters, <a href="/A081485/b081485.txt">Rows n=1..80 of triangle, flattened</a>

%e Triangle begins

%e 1

%e 1 3

%e 1 2 3

%e 1 3 5 7

%e 1 2 3 5 19

%e 1 3 5 7 13 19

%o Contribution from _Franklin T. Adams-Watters_, Apr 09 2009: (Start)

%o (PARI) arow(n) = {local(v, t, p, r);

%o if(n<=3,return(if(n==2,[1,3],if(n==3,[1,2,3],[1]))));

%o v=vector(n);v[1]=1;v[2]=if(n%2==0,3,2);t=v[2]+1;

%o for(i=3,n-2,v[i]=nextprime(v[i-1]+1);t+=v[i]);

%o p=nextprime(v[n-2]+1);

%o while(gcd(t+p,n)>1,p=nextprime(p+1));

%o v[n-1]=p;t+=p;r=p\n*n-t%n;

%o while(r<=p,r+=n);

%o while(!isprime(r),r+=n);

%o v[n]=r;v} (End)

%Y Cf. A081486, A081487, A081488.

%K nonn,tabl

%O 1,3

%A _Amarnath Murthy_, Mar 24 2003

%E Corrected and extended by _David Wasserman_, Jun 03 2004