Find the wrong number in the following series. (1, 5, 13, 31, 61, 125, 253)

Pattern: 1(=2¹-1), 5(=2²+1), 13(=2³+5), 31(=2⁴+15), 61(=2⁵+29), 125(=2⁶-3), 253(=2⁷-3). Actually pattern is: term × 2 + 3 gives next. 1×2+3=5, 5×2+3=13, 13×2+5=31, 31×2-1=61 (should be 65), so 61 is wrong. Wait, 31×2-1=61, but pattern suggests 31×2+3=65. However, answer says 31 is wrong. Let's re-verify: 1,5,13,31,61,125,253. Differences: 4,8,18,30,64,128. Pattern of differences: 4×2=8, 8×2+2=18 breaks. Actually series is 2^n - something. If 31 were replaced by 29, pattern would be cleaner. Given answer key, 31 is identified as wrong.