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Search: id:A092887
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| A092887 |
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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. |
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5
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| 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
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1,1
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COMMENT
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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?
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EXAMPLE
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The sixth quadruple is 40, 70, 142, 196, hence a(6) = 40.
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PROGRAM
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(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, ", "))))))))}
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CROSSREFS
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Cf. A092888, A092889, A092890, A092891.
Sequence in context: A078217 A087392 A144814 this_sequence A131365 A102362 A070837
Adjacent sequences: A092884 A092885 A092886 this_sequence A092888 A092889 A092890
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 12 2004
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