OFFSET
0,1
LINKS
IBM Research, Sibling triangles, Ponder This Challenge September 2024, asked for families with exactly 50 pairs.
Hugo Pfoertner, List of a(n) and A375749(n) for n=0..71.
EXAMPLE
n x=a(n)
| | y=A375749(n)
| | pairs of sides z leading to equal areas
0 2 1 only 1 triangle, no pair
1 7 4 [7,9]
2 15 10 [11,23], [17,19]
3 24 23 [19,43], [23,41], [29,37]
4 62 41 [45,95], [49,93], [59,87], [67,81]
PROG
(PARI) A(a, b, c) = (a+b+c)*(a+b-c)*(a-b+c)*(b+c-a); \\ squared area * 16
check(a, b) = {my(F=List()); for(c=a-b+1, a+b-1, listput(F, A(a, b, c))); F=vecsort(F); my(p=F[1], pc=1, mf=0); for(k=2, #F, if(F[k]==p, pc++; mf++, pc=1; p=F[k])); mf};
\\ returns [a(n), A375749(n)]
a375748_9(n) = for(a=2, oo, for(b=1, a-1, if(check(a, b)==n, return([a, b]))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Sep 09 2024
STATUS
approved