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A339637 Numbers congruent to 1 (mod 3) that are the quotient of two Cantor numbers (A005823). 1
1, 4, 7, 10, 13, 19, 22, 25, 28, 31, 34, 37, 40, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 163, 166, 169, 172, 175, 178, 181, 184, 187, 190, 193, 196, 199, 202, 205, 208, 211, 214, 217, 220, 223, 226, 229, 232 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..60.

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

Cf. A005823, A339636.

Sequence in context: A276874 A310685 A310686 * A173178 A348156 A287555

Adjacent sequences:  A339634 A339635 A339636 * A339638 A339639 A339640

KEYWORD

nonn

AUTHOR

Jeffrey Shallit, Dec 11 2020

STATUS

approved

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Last modified August 10 16:24 EDT 2022. Contains 356039 sequences. (Running on oeis4.)