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 A306231 #15 Feb 01 2019 05:04:06 %S A306231 1,2,3,6,4,5,20,8,9,72,16,7,14,21,78,32,11,352,64,10,40,15,24,12,30, %T A306231 35,390,48,96,51,102,60,13,832,117,144,18,168,42,28,39,180,56,84,63, %U A306231 70,780,120,26,128,19,504,36,288,126,45,112,151,896,156,720,224 %N A306231 Lexicographically earliest sequence of distinct positive terms such that for any n > 0 and any k > 0, floor((2^k) / a(n)) AND floor((2^k) / a(n+1)) = 0 (where AND denotes the bitwise AND operator). %C A306231 In other words, for any n > 0, the binary expansions of 1/a(n) and of 1/a(n+1) have no common one bit; in this sense, this sequence is similar to A109812. %C A306231 This sequence is a permutation of the natural numbers, with inverse A306233 (we can first prove that all the powers of 2 appear in the sequence and then that every natural number appear in the sequence). %H A306231 Rémy Sigrist, <a href="/A306231/b306231.txt">Table of n, a(n) for n = 1..2000</a> %H A306231 Rémy Sigrist, <a href="/A306231/a306231.gp.txt">PARI program for A306231</a> %H A306231 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a> %F A306231 For any n > 0, if A000120(a(n)) <> 1 and A000120(a(n+1)) <> 1, then gcd(A007733(a(n)), A007733(a(n+1))) > 1. %e A306231 The first terms, alongside A007733(a(n)) and the binary representation of 1/a(n) with periodic part in parentheses, are: %e A306231 n a(n) period bin(1/a(n)) %e A306231 -- ---- ------ ------------------- %e A306231 1 1 1 1.(0) %e A306231 2 2 1 0.1(0) %e A306231 3 3 2 0.(01) %e A306231 4 6 2 0.0(01) %e A306231 5 4 1 0.01(0) %e A306231 6 5 4 0.(0011) %e A306231 7 20 4 0.00(0011) %e A306231 8 8 1 0.001(0) %e A306231 9 9 6 0.(000111) %e A306231 10 72 6 0.000(000111) %e A306231 11 16 1 0.0001(0) %e A306231 12 7 3 0.(001) %e A306231 13 14 3 0.0(001) %e A306231 14 21 6 0.(000011) %e A306231 15 78 12 0.0(000001101001) %e A306231 16 32 1 0.00001(0) %e A306231 17 11 10 0.(0001011101) %e A306231 18 352 10 0.00000(0001011101) %e A306231 19 64 1 0.000001(0) %e A306231 20 10 4 0.0(0011) %o A306231 (PARI) See Links section. %Y A306231 Cf. A000120, A007733, A109812, A306233 (inverse). %K A306231 nonn,base %O A306231 1,2 %A A306231 _Rémy Sigrist_, Jan 30 2019