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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.
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
OFFSET
1,3
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
CROSSREFS
KEYWORD
nonn,tabl,more
AUTHOR
Amarnath Murthy, Mar 27 2003
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
STATUS
approved