A081521 Triangle read by rows: row n contains n terms in increasing order, relatively prime to n, whose sum is a multiple of n and such that the row contains the smallest possible subset of consecutive numbers starting with 1.
1, 1, 3, 1, 4, 7, 1, 3, 5, 7, 1, 2, 3, 6, 8, 1, 5, 7, 11, 13, 17, 1, 2, 3, 4, 5, 8, 12, 1, 3, 5, 7, 9, 11, 13, 15, 1, 2, 4, 5, 7, 8, 10, 13, 22, 1, 3, 7, 9, 11, 13, 17, 19, 21, 29, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 20
Offset: 1
Examples
Triangle begins: 1; 1, 3; 1, 4, 7; 1, 3, 5, 7; 1, 2, 3, 6, 8; 1, 5, 7, 11, 13, 17; 1, 2, 3, 4, 5, 8, 12; ...
Programs
-
PARI
row(n) = {my(m=n*(n-1)/2, v); forstep(k=m+n/(2-n%2), oo, n, v=List([]); for(i=2, k-m, if(gcd(n, i)==1, listput(v, i))); if(#v>n-2, forsubset([#v, n-1], w, if(r=1+sum(i=1, n-1, v[w[i]])==k, return(concat(1, vector(n-1, i, v[w[i]]))))))); } \\ Jinyuan Wang, May 24 2020
Extensions
New definition proposed by Omar E. Pol, Mar 24 2008, in an attempt to answer R. J. Mathar's questions.
Name corrected and more terms from Jinyuan Wang, May 24 2020
Comments