Star reduction among minimal length addition chains

An addition chain for a natural number n is a sequence 1 = a(0) < a(1) < ....< a(r) = n of minimal length of an addition chain for n is denoted by l(n). If j=i-1, then step is called a star step. We show that there is a minimal length addition chain for n such that the last four steps are stars. Then we conjecture that there is a minimal length addition chain for n such that the last [l(n)/2]-steps are stars. We verify that the conjecture is true for all numbers up to 2(18). An application of the result and the conjecture to generate a minimal length addition chain reduce the average CPU time by 23-29% and 38-58% respectively, and memory storage by 16-18% and 26-45% respectively for m-bit numbers with 14 <= m <= 22.