A395302 Numbers k that are a*b*c*r for some primitive Pythagorean triple (a,b,c) with inradius r such that 2*k +- 1 and 5*k +- 1 are twin prime pairs.

1799820, 32623271698080, 13128936616100760, 259392069521711280, 36315529922787340800, 117461585894352834420, 126565331933222396760, 1151453682528533014800, 2361939147567479394720, 3414380885231627520000, 4145418481480794015300, 7503058097835894835200, 16606374863882117957280

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..315

Example

a(1) = 1799820 is a term because it is the product of the sides (99, 20, 101) and inradius 9 of a primitive Pythagorean triple and 2*1799820+-1 = 3599639 and 3599641 and 3*1799820+-1 = 8999099 and 8999101 are all prime.

Maple

N:= 10^23: # for terms <= N
R:= {}:
for m from 1 while 2*(m-1)^2*(m+1)*m*(m^2+1) <= N do
  for n from 1 + (m mod 2) to m-1 by 2 do
    v:= 2*(m-n)^2 * (m+n)*m*n^2*(m^2+n^2);
    if v/(m-n)^2 > N then break fi;
    if v <= N and igcd(m, n) = 1 and andmap(isprime, [2*v-1, 2*v+1, 5*v-1, 5*v+1]) then
       R:= R union {v};
fi od od:
sort(convert(R, list));

Crossrefs

Intersection of A393526 and A395198.

Sequence in context: A234082 A140861 A234866 * A249196 A137819 A145537

Adjacent sequences: A395299 A395300 A395301 * A395303 A395304 A395305

Keyword

nonn

Author

Will Gosnell and Robert Israel, Apr 19 2026

Status

approved