OFFSET
1,1
EXAMPLE
a(3)=103 is in the sequence because 103 is a prime, the triangle with sides 103 and the next two primes 107 and 109 has area sqrt(382278435)/4 whose distance to the nearest integer, 4888, is approximately 0.0145, and this is less than any distance previously achieved.
MAPLE
atr:= proc(p, q, r) local s; s:= (p+q+r)/2; sqrt(s*(s-p)*(s-q)*(s-r)) end proc:
p:= 2: q:= 3: r:= 5: count:= 0: R:= NULL: dmin:= infinity:
while count < 10 do
p:= q; q:= r; r:= nextprime(r);
a:= atr(p, q, r);
d:= abs(a - round(a));
if is(d < dmin) then
count:= count+1;
dmin:= d;
R:= R, p;
fi;
od:
R;
PROG
(PARI) lista(nn) = {my(m=p=3, q=5, s, t); forprime(r=7, nn, s=sqrt((p-s=(p+q+r)/2)*(q-s)*(s-r)*s); if(m>t=min(s-floor(s), ceil(s)-s), print1(p, ", "); m=t); p=q; q=r); } \\ Jinyuan Wang, Oct 24 2020
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Robert Israel, Oct 19 2020
EXTENSIONS
a(13)-a(25) from Jinyuan Wang, Oct 24 2020
STATUS
approved