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<DIV>Here's another incorrect conjecture (although this one is at least marked as a conjecture). This basically states that a totally additive sequence (A064097) which is always >= the length of the shortest addition chain (A003313), never exceeds it by more than 1. But if A064097(n)-A003313(n)=1, A064097(n^2)-A003313(n^2)>=2. Since the first non-zero term in A076142 is a(23), at minimum a(529)>=2. (More generally, it follows that A076142 is unbounded.)</DIV>
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<DIV>My question is, what is the smallest n such that A064097(n)>=2? That way we can replace the conjecture with the smallest counterexample.</DIV>
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<DIV>Franklin T. Adams-Watters<BR>16 W. Michigan Ave.<BR>Palatine, IL 60067<BR>847-776-7645</DIV></DIV></DIV>
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