OFFSET
1,1
EXAMPLE
a(3)=5 is in the sequence because 5 is a prime, the triangle with sides 5, 7, 11 has area 3*sqrt(299)/4 whose distance to the nearest prime, 13, is approximately 0.0313, 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:
R:= 2, 3: p:= 3: q:= 5: r:= 7: count:= 2: dmin:= 7 - atr(3, 5, 7):
while count < 8 do
p:= q: q:= r: r:= nextprime(r);
a:= atr(p, q, r);
m:= round(a);
if not isprime(m) then next fi;
d:= abs(a-m);
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); print1(2); forprime(r=7, nn, s=sqrt((p-s=(p+q+r)/2)*(q-s)*(s-r)*s); if(m>t=min(s-precprime(s), nextprime(s)-s), print1(", ", p); m=t); p=q; q=r); } \\ Jinyuan Wang, Oct 24 2020
CROSSREFS
KEYWORD
nonn,more
AUTHOR
J. M. Bergot and Robert Israel, Oct 19 2020
EXTENSIONS
a(10)-a(16) from Jinyuan Wang, Oct 24 2020
STATUS
approved