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f=lambda n:"!"[:n]and(n>15and f(n/16)or"")+"HBKD"[n/4%4]+"OAEI"[n%4]
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A recursive solution. Try it on Ideone.
f=lambda n:"!"[:n]and f(n/16)+"HBKD"[n/4%4]+"OAEI"[n%4]
f=lambda n:(n>15and f(n/16)or"")+"HBKD"[n/4%4]+"OAEI"[n%4]
f=lambda n:(n>15and"!"[:n]and f(n/16)or"")+"HBKD"[n/4%4]+"OAEI"[n%4]
