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A390886

Numbers s such that there exists a triangle with integer sides, semiperimeter s and inradius r such that 2*s + r and 2*s - r are prime.

6, 20, 22, 28, 32, 38, 42, 48, 52, 54, 60, 66, 70, 72, 78, 84, 102, 104, 110, 114, 124, 128, 130, 136, 148, 162, 176, 182, 186, 190, 192, 198, 204, 208, 224, 228, 230, 238, 240, 244, 256, 262, 266, 276, 288, 294, 304, 308, 310, 316, 320, 326, 330, 336, 340, 350, 370, 374, 378, 380, 390, 392, 396

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OFFSET

1,1

COMMENTS

Numbers s such that there exist numbers a,b,c,r > 0 with s = (a+b+c)/2, r^2 = (s-a)*(s-b)*(s-c)/s, and 2*s + r and 2*s - r are prime.

All terms are even.

LINKS

Robert Israel, Table of n, a(n) for n = 1..1000

EXAMPLE

a(3) = 22 is a term because a triangle with sides 11, 13 and 20 has semiperimeter (11 + 13 + 20)/2 = 22 and inradius sqrt((22-11)*(22-13)*(22-20)/22) = 3, and 2*22 + 3 = 47 and 2*22 - 3 = 41 are both prime.

MAPLE

Res:= NULL: count:= 0:

for s from 2 to 1000 by 2 do

found:= false;

for a from 1 to 2*s/3 while not found do

for b from a to s - a/2 while not found do

c:= 2*s-a-b;

q:= (s-a)*(s-b)*(s-c)/s;

if q::integer and issqr(q) then

r:= sqrt(q);

if isprime(2*s+r) and isprime(2*s-r) then

found:= true; Res:= Res, s; count:= count+1;