cp's OEIS Frontend

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

%I A108944 #9 Apr 09 2025 16:16:28
%S A108944 1,4,1,0,4,16,1,0,196,9,400,100,1,16,4,169,4,36,1936,1,529,1,36,100,
%T A108944 400,16,25,10000,10816,49,144,17956,25,400,0,169,961,16,2500,25,0,676,
%U A108944 3844,784,100,64,169,121,400,49,3025,9,17689,78400,400,20449,100,96100,361
%N A108944 Minimal square k^2 such that sum of the n-th twin prime pair plus k^2 is a square.
%H A108944 Robert Israel, <a href="/A108944/b108944.txt">Table of n, a(n) for n = 1..10000</a>
%F A108944 a(n) = A108945(n) - A001359(n) - A006512(n).
%F A108944 a(n) = (A033677(A040040(n)) - A040040(n)/A033677(A040040(n)))^2. - _Robert Israel_, Apr 09 2025
%p A108944 P:= select(isprime,{seq(i,i=3..10^4,2)}):
%p A108944 TA:= sort((convert((P intersect (P +~ 2)),list) -~ 1)/~ 2):
%p A108944 f:= proc(m) local d;
%p A108944   for d in sort(convert(numtheory:-divisors(m),list)) do
%p A108944     if d^2 >= m then return (d - m/d)^2 fi
%p A108944   od
%p A108944 end proc:
%p A108944 map(f, TA); # _Robert Israel_, Apr 09 2025
%Y A108944 Cf. A001359, A006512, A033677, A040040, A108943, A108945.
%K A108944 nonn
%O A108944 1,2
%A A108944 _Giovanni Teofilatto_, Jul 21 2005
%E A108944 Edited and extended by _Ray Chandler_, Jul 25 2005