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 A300428 #20 Mar 11 2018 10:09:06 %S A300428 1,1,5,1,3,5,9,1,5,3,11,5,11,9,17,1,9,7,5,11,3,13,11,9,5,11,13,9,11, %T A300428 17,33,1,17,11,9,7,19,5,13,11,29,3,19,13,27,11,19,17,9,19,5,11,19,13, %U A300428 29,9,19,11,13,17,25,33,65,1,33,23,17,13,11,29,9,23,7 %N A300428 a(n) is the least positive k such that the binary representation of n appears as a substring in the binary representation of 1/k (ignoring the radix point and adding trailing zeros if necessary in case of a terminating expansion). %C A300428 In other words, a(n) is the least k > 0 such that floor((2^i) / k) mod A062383(n) = n for some integer i >= 0. %C A300428 This sequence is similar to A035335 for the base 2. %C A300428 All terms are odd. %C A300428 All terms appears infinitely many times (as a(n) equals at least a(2*n) or a(2*n + 1)). %C A300428 See also A300475 for a similar sequence. %H A300428 Rémy Sigrist, <a href="/A300428/b300428.txt">Table of n, a(n) for n = 1..8191</a> %H A300428 Rémy Sigrist, <a href="/A300428/a300428.gp.txt">PARI program for A300428</a> %F A300428 a(2^k) = 1 for any k >= 0. %F A300428 a(2^k - 1) = 2^k + 1 for any k > 1. %F A300428 a(A000975(k)) = 3 for any k > 2. %F A300428 a(A033138(k)) = 7 for any k > 4. %F A300428 a(n) <= A300475(n) for any n > 0. %e A300428 The first terms, alongside the binary representation of 1/a(n) with the earliest occurrence of the binary representation of n in parentheses, are: %e A300428 n a(n) bin(1/a(n)) %e A300428 -- ---- ----------- %e A300428 1 1 (1).000... %e A300428 2 1 (1.0)000... %e A300428 3 5 0.00(11)001... %e A300428 4 1 (1.00)000... %e A300428 5 3 0.0(101)010... %e A300428 6 5 0.00(110)011... %e A300428 7 9 0.000(111)000... %e A300428 8 1 (1.000)000... %e A300428 9 5 0.001(1001)100... %e A300428 10 3 0.0(1010)101... %e A300428 11 11 0.000(1011)101... %e A300428 12 5 0.00(1100)110... %e A300428 13 11 0.000101(1101)000... %e A300428 14 9 0.000(1110)001... %e A300428 15 17 0.0000(1111)000... %e A300428 16 1 (1.0000)000... %e A300428 17 9 0.00011(10001)110... %e A300428 18 7 0.00(10010)010... %e A300428 19 5 0.001(10011)001... %e A300428 20 11 0.0001011(10100)010... %o A300428 (PARI) See Links section. %Y A300428 Cf. A000975, A033138, A035335, A062383, A300475. %K A300428 nonn,base %O A300428 1,3 %A A300428 _Rémy Sigrist_, Mar 05 2018