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

1,3

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

Links

Table of n, a(n) for n=1..66.

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

Cf. A081522, A081523, A081524.

Sequence in context: A049918 A357182 A028861 * A213224 A210218 A086273

Adjacent sequences: A081518 A081519 A081520 * A081522 A081523 A081524

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