A070105 - OEIS

%I #10 Jul 27 2024 04:02:40

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,

%T 2,0,1,0,2,0,1,0,2,0,0,0,3,0,1,0,1,0,2,0,0,0,0,0,3,0,1,0,3,0,4,0,3,0,

%U 1,0,1,0,1,0,1,0,2,0,3,0,1,0,5,0,4,0,5,0,5,0

%N Number of integer triangles with perimeter n and prime side lengths which are obtuse and scalene.

%C a(n) = 0 if n is even. - _Robert Israel_, Jul 26 2024

%H Robert Israel, <a href="/A070105/b070105.txt">Table of n, a(n) for n = 1..10000</a>

%H R. Zumkeller, <a href="/A070080/a070080.txt">Integer-sided triangles</a>

%p f:= proc(n) local a,b,q,bmin,bmax,t;

%p   t:= 0;

%p   if n::even then return 0 fi;

%p   for a from 1 to n/3 by 2 do

%p     if not isprime(a) then next fi;

%p     bmin:= max(a+1,(n+1)/2-a); if bmin::even then bmin:= bmin+1 fi;

%p     q:= (n^2-2*n*a)/(2*(n-a));

%p     if q::integer then bmax:= min((n-a)/2, q-1) else bmax:= min((n-a)/2, floor(q)) fi;

%p     t:= t + nops(select(b -> isprime(b) and isprime(n-a-b), [seq(b,b=bmin .. bmax,2)]))

%p   od;

%p   t

%p end proc:

%p map(f, [$1..100]); # _Robert Israel_, Jul 26 2024

%Y Cf. A070080, A070081, A070082, A070101, A005044, A070088, A070090, A070103, A024156, A070132.

%K nonn,look

%O 1,35

%A _Reinhard Zumkeller_, May 05 2002