The transition in $He^+$ ion that would have the same wave number as the first Lyman line in hydrogen spectrum is
$ \bar \nu = R Z ^2 [ { 1 \over n ^2 _1 } - { 1 \over n ^2 _f } ]cm ^ {-1} $ $ \bar \nu_H = R [ { 1 \over n ^2 _1 } - { 1 \over n ^2 _f } ]cm ^ {-1} $ $ \bar \nu_{He} = R Z ^2 [ { 1 \over n ^2 _1 } - { 1 \over n ^2 _f } ]cm ^ {-1} $