This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A326538 #10 Jul 14 2019 18:02:08 %S A326538 1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,7,1,3,3,3,3, %T A326538 23,1,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, %U A326538 1,1,1,1,1,1,1,1,1,1,1,1,1,1,15,1,7,7 %N A326538 a(n) is the numerator of the image of 1/n by the Cantor staircase function. %C A326538 The Cantor staircase function, say c, maps rational numbers in the interval [0..1] to rational numbers in the interval [0..1], hence this sequence is well defined. %C A326538 For any n > 0, the binary expansion of c(1/n) is terminating (and A326539(n) is a power of 2) iff the ternary expansion of 1/n is terminating or contains a digit 1. %H A326538 Rémy Sigrist, <a href="/A326538/b326538.txt">Table of n, a(n) for n = 1..6561</a> %H A326538 Rémy Sigrist, <a href="/A326538/a326538.gp.txt">PARI program for A326538</a> %H A326538 Wikipedia, <a href="https://en.wikipedia.org/wiki/Cantor_function">Cantor function</a> %e A326538 The first terms, alongside c(1/n) and the ternary and binary representation of 1/n and c(1/n), respectively, with periodic part in parentheses, are: %e A326538 n a(n) c(1/n) ter(1/n) bin(c(1/n)) %e A326538 -- ---- ------ ---------------------- ----------- %e A326538 1 1 1 1.(0) 1.(0) %e A326538 2 1 1/2 0.(1) 0.1(0) %e A326538 3 1 1/2 0.1(0) 0.1(0) %e A326538 4 1 1/3 0.(02) 0.(01) %e A326538 5 1 1/4 0.(0121) 0.01(0) %e A326538 6 1 1/4 0.0(1) 0.01(0) %e A326538 7 1 1/4 0.(010212) 0.01(0) %e A326538 8 1 1/4 0.(01) 0.01(0) %e A326538 9 1 1/4 0.01(0) 0.01(0) %e A326538 10 1 1/5 0.(0022) 0.(0011) %e A326538 11 3 3/16 0.(00211) 0.0011(0) %e A326538 12 1 1/6 0.0(02) 0.0(01) %e A326538 13 1 1/7 0.(002) 0.(001) %e A326538 14 1 1/8 0.(001221) 0.001(0) %e A326538 15 1 1/8 0.0(0121) 0.001(0) %e A326538 16 1 1/8 0.(0012) 0.001(0) %e A326538 17 1 1/8 0.(0011202122110201) 0.001(0) %e A326538 18 1 1/8 0.00(1) 0.001(0) %e A326538 19 1 1/8 0.(001102100221120122) 0.001(0) %e A326538 20 1 1/8 0.(0011) 0.001(0) %o A326538 (PARI) See Links section. %Y A326538 See A326539 for the corresponding denominators. %Y A326538 Cf. A061392. %K A326538 nonn,base,frac %O A326538 1,11 %A A326538 _Rémy Sigrist_, Jul 12 2019