In the following number series, one number is wrong. Find that wrong number. 12, 16, 23, 50, 99, 220, 389

The series is 12, 16, 23, 50, 99, 220, 389. Pattern: +4, +7, +27, +49, +121, +169. The additions are squares: 4=2², 7(not a square), 27(not a square), 49=7², 121=11², 169=13². Better pattern: differences of differences: 7-4=3, 27-7=20, 49-27=22, 121-49=72... not clean. Try: 12+4=16, 16+7=23, 23+27=50, 50+49=99, 99+121=220, 220+169=389. The additions 4, 7, 27, 49, 121, 169 - prime squares except 7 and 27. If pattern was 2², 3², 5², 7², 11², 13² = 4, 9, 25, 49, 121, 169 then: 12+4=16, 16+9=25 (not 23), 25+25=50, 50+49=99, etc. So 23 is wrong.