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%I #10 Jul 14 2019 18:02:08
%S 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 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 1,1,1,1,1,1,1,1,1,1,1,1,1,1,15,1,7,7
%N a(n) is the numerator of the image of 1/n by the Cantor staircase function.
%C 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 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 Rémy Sigrist, <a href="/A326538/b326538.txt">Table of n, a(n) for n = 1..6561</a>
%H Rémy Sigrist, <a href="/A326538/a326538.gp.txt">PARI program for A326538</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Cantor_function">Cantor function</a>
%e 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 n a(n) c(1/n) ter(1/n) bin(c(1/n))
%e -- ---- ------ ---------------------- -----------
%e 1 1 1 1.(0) 1.(0)
%e 2 1 1/2 0.(1) 0.1(0)
%e 3 1 1/2 0.1(0) 0.1(0)
%e 4 1 1/3 0.(02) 0.(01)
%e 5 1 1/4 0.(0121) 0.01(0)
%e 6 1 1/4 0.0(1) 0.01(0)
%e 7 1 1/4 0.(010212) 0.01(0)
%e 8 1 1/4 0.(01) 0.01(0)
%e 9 1 1/4 0.01(0) 0.01(0)
%e 10 1 1/5 0.(0022) 0.(0011)
%e 11 3 3/16 0.(00211) 0.0011(0)
%e 12 1 1/6 0.0(02) 0.0(01)
%e 13 1 1/7 0.(002) 0.(001)
%e 14 1 1/8 0.(001221) 0.001(0)
%e 15 1 1/8 0.0(0121) 0.001(0)
%e 16 1 1/8 0.(0012) 0.001(0)
%e 17 1 1/8 0.(0011202122110201) 0.001(0)
%e 18 1 1/8 0.00(1) 0.001(0)
%e 19 1 1/8 0.(001102100221120122) 0.001(0)
%e 20 1 1/8 0.(0011) 0.001(0)
%o (PARI) See Links section.
%Y See A326539 for the corresponding denominators.
%Y Cf. A061392.
%K nonn,base,frac
%O 1,11
%A _Rémy Sigrist_, Jul 12 2019
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