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 A300475 #16 Mar 11 2018 17:52:08 %S A300475 1,1,5,1,3,5,9,1,7,3,11,5,19,9,17,1,15,7,13,25,3,23,11,21,5,19,37,9, %T A300475 35,17,33,1,31,15,29,7,27,53,13,25,49,3,47,23,45,11,43,21,41,81,5,39, %U A300475 19,75,37,9,71,35,69,17,67,33,65,1,63,31,61,15,59,29,57 %N A300475 a(n) is the least positive k such that the binary representation n appears in front of the binary representation of 1/k (ignoring the radix point and the leading zeros and adding trailing zeros if necessary in case of a terminating expansion). %C A300475 In other words, a(n) is the least k > 0 such that floor((2^i) / k) = n for some integer i >= 0. %C A300475 This sequence is similar to A095156 for the base 2. %C A300475 All terms are odd. %C A300475 All terms appears infinitely many times (as a(n) equals at least a(2*n) or a(2*n + 1)). %C A300475 See also A300428 for a similar sequence. %H A300475 Rémy Sigrist, <a href="/A300475/b300475.txt">Table of n, a(n) for n = 1..10000</a> %H A300475 Rémy Sigrist, <a href="/A300475/a300475.gp.txt">PARI program for A300475</a> %H A300475 Rémy Sigrist, <a href="/A300475/a300475.png">Colored logarithmic scatterplot of the first 1000000 terms</a> (where the color is function of A070939(n * a(n))) %F A300475 a(2^k) = 1 for any k >= 0. %F A300475 a(2^k - 1) = 2^k + 1 for any k > 1. %F A300475 a(A000975(k)) = 3 for any k > 2. %F A300475 a(A033138(k)) = 7 for any k > 4. %F A300475 a(n) >= A300428(n). %e A300475 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 A300475 n a(n) bin(1/a(n)) %e A300475 -- ---- ----------- %e A300475 1 1 (1).000... %e A300475 2 1 (1.0)000... %e A300475 3 5 0.00(11)001... %e A300475 4 1 (1.00)000... %e A300475 5 3 0.0(101)010... %e A300475 6 5 0.00(110)011... %e A300475 7 9 0.000(111)000... %e A300475 8 1 (1.000)000... %e A300475 9 7 0.00(1001)001... %e A300475 10 3 0.0(1010)101... %e A300475 11 11 0.000(1011)101... %e A300475 12 5 0.00(1100)110... %e A300475 13 19 0.0000(1101)011... %e A300475 14 9 0.000(1110)001... %e A300475 15 17 0.0000(1111)000... %e A300475 16 1 (1.0000)000... %e A300475 17 15 0.000(10001)000... %e A300475 18 7 0.00(10010)010... %e A300475 19 13 0.000(10011)101... %e A300475 20 25 0.0000(10100)011... %o A300475 (PARI) See Links section. %Y A300475 Cf. A000975, A033138, A070939, A095156, A300428. %K A300475 nonn,look,base %O A300475 1,3 %A A300475 _Rémy Sigrist_, Mar 06 2018