A282241 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.

62, 89, 101, 122, 134, 146, 150, 161, 173, 185, 189, 203, 206, 209, 218, 230, 234, 248, 254, 257, 266, 269, 270, 278, 281, 285, 299, 305, 314, 317, 321, 326, 329, 338, 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

Offset

1,1

Comments

This sequence is subsequence of A004432 and A024804.

q-p is even, and b-a is multiple of 3, because 3(q-p)=2(b-a).

Links

Table of n, a(n) for n=1..60.

Example

122 = (5-1)^2+5^2+(5+4)^2 = (7-4)^2+7^2+(7+1)^2, with symmetrical differences 1 and 4.
248 = (6-2)^2+6^2+(6+8)^2 = (10-8)^2+10^2+(10+2)^2, with a=2, b=8.

Prog

(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
for(i=3, 500, if(is_sym_sum(i), print1(i, ", ")))

Crossrefs

Cf. A004432, A024796, A024804.

Sequence in context: A039479 A118156 A214252 * A114966 A104078 A136774

Adjacent sequences: A282238 A282239 A282240 * A282242 A282243 A282244

Keyword

nonn

Author

Antonio Roldán, Feb 09 2017

Status

approved