A108944 Minimal square k^2 such that sum of the n-th twin prime pair plus k^2 is a square.

1, 4, 1, 0, 4, 16, 1, 0, 196, 9, 400, 100, 1, 16, 4, 169, 4, 36, 1936, 1, 529, 1, 36, 100, 400, 16, 25, 10000, 10816, 49, 144, 17956, 25, 400, 0, 169, 961, 16, 2500, 25, 0, 676, 3844, 784, 100, 64, 169, 121, 400, 49, 3025, 9, 17689, 78400, 400, 20449, 100, 96100, 361

Offset: 1

Author

Giovanni Teofilatto, Jul 21 2005

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001359, A006512, A033677, A040040, A108943, A108945.

Programs

Maple

P:= select(isprime,{seq(i,i=3..10^4,2)}):
TA:= sort((convert((P intersect (P +~ 2)),list) -~ 1)/~ 2):
f:= proc(m) local d;
  for d in sort(convert(numtheory:-divisors(m),list)) do
    if d^2 >= m then return (d - m/d)^2 fi
  od
end proc:
map(f, TA); # Robert Israel, Apr 09 2025

Formula

a(n) = A108945(n) - A001359(n) - A006512(n).

a(n) = (A033677(A040040(n)) - A040040(n)/A033677(A040040(n)))^2. - Robert Israel, Apr 09 2025

Extensions

Edited and extended by Ray Chandler, Jul 25 2005