OFFSET

1,2

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. 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 additional "sporadic" counterexamples enumerated by A339636, whose structure is not well understood.

A simple automaton-based (or breadth-first search) algorithm can establish in O(n) time whether n is in A or not.

LINKS

J. S. Athreya, B. Reznick, and J. T. Tyson, Cantor set arithmetic, Amer. Math. Monthly 126 (2019), 4-17.

James Haoyu Bai, Joseph Meleshko, Samin Riasat, and Jeffrey Shallit, Quotients of Palindromic and Antipalindromic Numbers, arXiv:2202.13694 [math.NT], 2022.

EXAMPLE

106 is in the sequence, because 106=1462376/13796, and 1462376 in base 3 is 2202022000002, and 13796 in base 3 is 200220222.

CROSSREFS

KEYWORD

nonn

AUTHOR

Jeffrey Shallit, Dec 11 2020

STATUS

approved