A382931 Numbers k for which the Pythagorean triangle (A046083(k), A046084(k), A009000(k)) has an integer altitude.
7, 19, 36, 51, 69, 88, 99, 106, 126, 147, 163, 187, 196, 208, 227, 240, 250, 273, 293, 314, 342, 361, 384, 392, 409, 434, 455, 459, 483, 504, 507, 525, 549, 552, 579, 599, 627, 649, 679, 702, 711, 718, 724, 744, 752, 775, 802, 829, 854, 879, 894, 908, 935, 960
Offset: 1
Keywords
Examples
7 is in the sequence because the pythagorean triangle (A046083(7), A046084(7), A009000(7)) = (15, 20, 25) has the integer altitude 15*20/25 = 12.
Links
- Felix Huber, Table of n, a(n) for n = 1..10000
- Eric Weisstein's World of Mathematics, Pythagorean Triple
Programs
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Maple
A382931:=proc(H) # All hypotenuses <= H. local a,b,c,k,p,q,L,M; L:=[]; M:=[]; for p from 2 to floor(sqrt(H-1)) do for q to min(p-1,floor(sqrt(H-p^2))) do if gcd(p,q)=1 and is(p-q,odd) then a:=p^2-q^2; b:=2*p*q; c:=p^2+q^2; for k to iquo(H,c) do L:=[op(L),[k*c,k*max(a,b),k*a*b/c]] od fi od od; L:=sort(L); for k to nops(L) do if is(L[k,3],integer) then M:=[op(M),k] fi od; return op(M) end proc; A382931(1075);
Comments