

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
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OFFSET

1,3


COMMENTS

The "smallest set of n distinct numbers" is not a welldefined 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*(n1)/2, v); forstep(k=m+n/(2n%2), oo, n, v=List([]); for(i=2, km, if(gcd(n, i)==1, listput(v, i))); if(#v>n2, forsubset([#v, n1], w, if(r=1+sum(i=1, n1, v[w[i]])==k, return(concat(1, vector(n1, i, v[w[i]]))))))); } \\ Jinyuan Wang, May 24 2020


CROSSREFS

Cf. A081522, A081523, A081524.
Sequence in context: A170839 A049918 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



