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%I #9 Feb 04 2018 03:30:21
%S 62,89,101,122,134,146,150,161,173,185,189,203,206,209,218,230,234,
%T 248,254,257,266,269,270,278,281,285,299,305,314,317,321,326,329,338,
%U 341,342,347,356,357,362,374,377,378,386,389,398,401,404,405,414,419,422,425,426,434,437,441,446,449,458
%N Numbers that are the sum of 3 distinct nonzero squares in two ways with symmetrical differences: a(n) = (p-a)^2+p^2+(p+b)^2 = (q-b)^2+q^2+(q+a)^2, p, q, a, b, positive integer, a<b, p<q.
%C This sequence is subsequence of A004432 and A024804.
%C q-p is even, and b-a is multiple of 3, because 3(q-p)=2(b-a).
%e 122 = (5-1)^2+5^2+(5+4)^2 = (7-4)^2+7^2+(7+1)^2, with symmetrical differences 1 and 4.
%e 248 = (6-2)^2+6^2+(6+8)^2 = (10-8)^2+10^2+(10+2)^2, with a=2, b=8.
%o (PARI) is_sym_sum(n)=local(x,e=0,a,b,p);x=1;while(x^2<n\3&&e==0,a=1;while(x^2+(x+a)^2<n&&e==0,z=n-x^2-(x+a)^2; if(issquare(z),z=sqrtint(z);b=z-x-a;if(b>a,p=1;while(p^2<=n/3&&e==0,if(p^2+(p+b)^2+(p+a+b)^2==n,e=1);p+=1)));a+=1);x+=1);e
%o for(i=3,500,if(is_sym_sum(i),print1(i,", ")))
%Y Cf. A004432, A024796, A024804.
%K nonn
%O 1,1
%A _Antonio Roldán_, Feb 09 2017
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