

A092889


Third 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.


4



40, 97, 128, 88, 96, 142, 151, 164, 238, 237, 189, 184, 174, 212, 304, 295, 268, 256, 350, 279, 350, 320, 374, 308, 443, 328, 475, 329, 290, 394, 416, 367, 470, 686, 517, 438, 585, 605, 640, 620, 572, 498, 736, 455, 435, 650, 502, 635, 625, 605, 846, 891
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OFFSET

1,1


COMMENTS

Suggested by Thomas A. Nagy.  A092887 gives first component, A092888 gives second component, A092890 gives fourth component.


LINKS

Table of n, a(n) for n=1..52.


EXAMPLE

The fourth quadruple is 56, 63, 88, 171, hence a(4) = 88.


PROG

(PARI) {m=1110; for(n=6, m, for(a=1, (n3)\3, for(b=a+1, (na1)\2, c=nab; 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(c, ", "))))))))}


CROSSREFS

Cf. A092887, A092888, A092890, A092891.
Sequence in context: A063310 A211493 A185791 * A235280 A235271 A033832
Adjacent sequences: A092886 A092887 A092888 * A092890 A092891 A092892


KEYWORD

nonn


AUTHOR

Klaus Brockhaus, Mar 12 2004


STATUS

approved



