A092887 First component of quadruples a,b,c,d such that a < b < c < d, (a*b*c) mod (a+b+c) = d, (a*b*d) mod (a+b+d) = c, (a*c*d) mod (a+c+d) = b, (b*c*d) mod (b+c+d) = a. The quadruples are ordered according to sum of first three components, secondary by first component, thirdly by second component.

10, 13, 12, 56, 48, 40, 49, 23, 29, 47, 45, 46, 70, 69, 70, 79, 40, 34, 92, 117, 56, 128, 102, 176, 38, 160, 19, 98, 125, 16, 20, 79, 110, 56, 130, 70, 90, 77, 124, 15, 65, 90, 124, 195, 270, 65, 205, 23, 35, 209, 78, 58, 237, 33, 70, 304, 91, 286, 176, 274, 238, 238, 28

Offset

1,1

Comments

Suggested by Thomas A. Nagy. - A092888 gives second component, A092889 gives third component, A092890 gives fourth component.

Problem: Which numbers will never appear as one of the components of those quadruples?

Links

Table of n, a(n) for n=1..63.

Example

The sixth quadruple is 40, 70, 142, 196, hence a(6) = 40.

Prog

(PARI) {m=1320; for(n=6, m, for(a=1, (n-3)\3, for(b=a+1, (n-a-1)\2, c=n-a-b; d=a*b*c%(a+b+c); if(c<d, if(a*b*d%(a+b+d)==c, if(a*c*d%(a+c+d)==b, if(b*c*d%(b+c+d)==a, print1(a, ", "))))))))}

Crossrefs

Cf. A092888, A092889, A092890, A092891.

Sequence in context: A332478 A144814 A241174 * A131365 A241144 A102362

Adjacent sequences: A092884 A092885 A092886 * A092888 A092889 A092890

Keyword

nonn

Author

Klaus Brockhaus, Mar 12 2004

Status

approved