A056131 Sequence A001033 gives the numbers n such that the sum of the squares of n consecutive odd numbers x^2 + (x+2)^2 + ... +(x+2n-2)^2 = k^2 for some integer k. For each n, this sequence gives the least value of x.

1, 27, 27, 91, 151, 225, 31, 67, 14037, 47, 119, 4177, 165, 103, 3599, 291, 11467887, 3089, 1297, 379, 57, 131, 110311, 153, 2637, 353, 163, 1679, 1211, 995, 54863, 105, 43, 615, 439, 15, 12955, 2263, 11661, 1867, 1281, 1433, 46671, 303, 21139, 324545, 4159, 343803