A096087 Triangle read by rows: row n lists cubic remainders modulo n.

0, 1, 0, 1, 2, 0, 1, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 1, 6, 0, 1, 3, 5, 7, 0, 1, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 3, 4, 5, 7, 8, 9, 11, 0, 1, 5, 8, 12, 0, 1, 6, 7, 8, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 3, 5, 7, 8, 9, 11, 13, 15, 0, 1, 2, 3

Offset: 2

Author

Cino Hilliard, Jul 21 2004

Keywords

• nonn
• tabf

Comments

Modulo 7 and 9 there are surprisingly few cubic remainders.

Examples

			Irregular array begins:
0, 1;
0, 1, 2;
0, 1, 3;
0, 1, 2, 3, 4;
0, 1, 2, 3, 4, 5;
0, 1, 6;
0, 1, 3, 5, 7;
0, 1, 8;
0, 1, 2, 3, 4, 5, 6, 7, 8, 9;
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10;
		

Crossrefs

Cf. A096107.

Programs

PARI

maybecube(n) = { for(x=2,n, b=floor(x-1); a=vector(b+1); for(y=1,b, z=y^3%x; if(z<>0, a[y]=z; ) ); s=vecsort(a); c=1; print1(s[1]","); for(j=2,b+1, if(s[j]<>s[j-1], c++; print1(s[j]",") ) ); ) }

Extensions

Edited by Don Reble, May 07 2006