|
%I #6 Mar 14 2015 09:56:17
%S 1,0,0,4,2,0,0,0,0,0,0,10,4,4,2,6,2,4,2,0,0,4,10,0,6,4,0,4,8,2,6,0,2,
%T 2,2,6,6,0,0,6,2,0,2,8,4,0,0,12,4,6,10,14,2,2,28,4,4,2,6,8,2,2,0,4,14,
%U 20,10,4,0,8,6,0,4,2,14,0,4,8,0,4,4,16,10,12,2,2,0,0,2,6,8,20,6,20,6,2,2,0
%N Absolute difference between the sums of the left and right diagonals of ordered 2 X 2 prime squares.
%C The first 2 X 2 prime square of a set of ordered 2 X 2 prime squares begins with 2. Just a 2 X 2 prime square is any 4 consecutive primes arranged in a square formation.
%F A 2 X 2 ordered prime square is 4 consecutive primes arranged in a square of the form p(4n-3) p(4n-2) p(4n-1) p(4n) where n=1, 2, ... and Left diagonal is p(4n+1), p(4n) Right diagonal is p(4n+2), p(4n+3).
%e The 4th prime square is
%e 41 43
%e 47 53
%e sum of left diagonal = 41+53 = 94
%e sum of right diagonal = 43+47 = 90
%e difference = 4
%e So 4 is the 4th term.
%o (PARI) diffdiag(n) = { local(x,d1,d2); forstep(x=1,n,4, d1=prime(x)+ prime(x+3); d2=prime(x+1)+ prime(x+2); print1((abs(d1-d2)",") ) }
%K easy,nonn
%O 1,4
%A _Cino Hilliard_, Apr 07 2005
|
