

A339636


Counterexamples to a conjecture about integers representable as the quotient of two Cantor numbers (A005823).


1




OFFSET

1,1


COMMENTS

Let C be the Cantor numbers (A005823), and let A be the set of integers congruent to 1 (mod 3) representable as the quotient of two nonzero elements of C (A339637). It is easy to see that if (3/2)*3^i < n < 2*3^i for some i, then n cannot be in A. Initial empirical data suggested that these are the only integers congruent to 1 (mod 3) not in A. However, there are "sporadic" counterexamples enumerated by this sequence entry, whose structure is not well understood.
A simple automatonbased (or breadthfirst search) algorithm can establish in O(n) time whether n is in A or not.
Conjecture: every number of the form 23*3^(4k+3)  20 is not representable. In addition to numbers already in the sequence, for k = 3 this gives 330024841, which is also not representable.


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KEYWORD

nonn,more


AUTHOR



STATUS

approved



