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1
1, 2, 4, 4, 4, 9, 5, 8, 8, 13, 7
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.
+10
5
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
COMMENTS
The "smallest set of n distinct numbers" is not a well-defined term in the definition. Why is row 5 "1,2,3,6,8" but not "1,2,4,6,7"? Why is row 7 "1,2,3,4,5,8,12" but not "1,2,4,5,6,8,9"? - R. J. Mathar, Nov 12 2006
EXAMPLE
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;
...
PROG
(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
Name corrected and more terms from Jinyuan Wang, May 24 2020
1, 3, 7, 7, 8, 17, 12, 15, 22, 29, 20
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