

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.


4



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
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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, (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(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



