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Sum of the sides of ordered 2 X 2 prime squares.
0

%I #6 Mar 14 2015 09:56:55

%S 34,120,240,368,516,648,816,960,1152,1320,1488,1660,1856,2024,2196,

%T 2388,2596,2816,3004,3192,3408,3576,3740,3960,4188,4472,4656,4840,

%U 5016,5204,5388,5640,5884,6076,6332,6564,6756,6960,7176,7452,7676,7896,8124,8304

%N Sum of the sides 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 sides are as follows s1 = p(4n-3) p(4n-2) s2 = p(4n-1) p(4n) s3 = p(4n-3) p(4n-1) s4 = p(4n-2) p(4n).

%e The 4th prime square is

%e 41 43

%e 47 53

%e s1 = 41+43 = 84

%e s2 = 47+53 = 100

%e s3 = 41+47 = 88

%e s4 = 43+53 = 96

%e sum = 368

%e So 368 is the 4th term.

%o (PARI) sumsides(n) = { local(x,s1,s2,s3,s4); forstep(x=1,n,4, s1=prime(x)+ prime(x+1); s2=prime(x+2)+ prime(x+3); s3=prime(x)+ prime(x+2); s4=prime(x+1)+ prime(x+3); print1(s1+s2+s3+s4",") ) }

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, Apr 07 2005