A076142

[franktaw at netscape.net]

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.)
 
My question is, what is the smallest n such that A064097(n)>=2?  That way we can replace the conjecture with the smallest counterexample.
 
Franklin T. Adams-Watters
16 W. Michigan Ave.
Palatine, IL 60067
847-776-7645
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