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 A303763 #20 May 02 2018 22:36:14 %S A303763 0,1,3,2,7,4,5,15,6,31,8,9,11,10,63,12,13,127,14,255,16,17,19,18,23, %T A303763 20,21,511,22,1023,24,25,27,26,2047,28,29,4095,30,8191,32,33,35,34,39, %U A303763 36,37,47,38,16383,40,41,43,42,32767,44,45,65535,46,131071,48,49,51,50,55,52,53,262143,54,524287,56,57,59,58,1048575,60,61 %N A303763 Permutation of nonnegative integers: a(0) = 0 and for n > 0, a(n) = the least k for which bitor(k,a(n-1)) = a(n-1) and k is not already present, and otherwise, if no such k exists, the least number not already present that can be obtained by cumulatively filling the successive vacant bits of a(n-1) from its least significant end (by toggling 0's to 1's, possibly also one or more leading zeros). %C A303763 Shares with permutations like A003188, A006068, A300838, A302846, A303765, and A303767 the property that when moving from any a(n) to a(n+1) either a subset of 0-bits are toggled on (changed to 1's), or a subset of 1-bits are toggled off (changed to 0's), but no both kind of changes may occur at the same step. %H A303763 Antti Karttunen, <a href="/A303763/b303763.txt">Table of n, a(n) for n = 0..2047</a> %H A303763 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a> %H A303763 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a> %e A303763 For a(2), a(1) = 1, and the only subset mask (a number k for which bitor(k,1) = k) is 1 itself, already present, so we start toggling 0's to 1's with binary expansion "...00001" of 1, and we get "11" (= binary representation of 3), and 3 is not yet present, thus a(2) = 3. %e A303763 For a(3), previous a(2) = 3, "...011" in binary, and "10" (= 2) is the least submask that is not already present, thus a(3) = 2. %e A303763 For a(4), previous = 2, "...010" in binary, and there are no submasks that are not already used, thus we start toggling 0's to 1's from the right, and "11" (3) is already present, but "111" (7) is not, thus a(4) = 7. %e A303763 For a(5), previous = 7, with seven submasks "1", "10", "11", "100", "101", "110", "111" (binary representations for 1 - 7), and "100" = 4 is the least one of these not already present, thus a(5) = 4. %e A303763 For a(6), previous = 4, "..0100" in binary, and no submasks that wouldn't have been already used, thus by toggling from the right, we first obtain "...0101" = 5, which is still free, so a(6) = 5. %e A303763 For a(7), previous = 5, "..0101" in binary, and no submasks that would be free (both 1 and 4 are already present), thus by toggling zeros from the right, we first obtain "...0111" = 7, which also has been used, so we continue filling the zeros, to obtain next "...1111" = 15, which is still free, so a(7) = 15. %e A303763 For a(8), previous = 15, "..1111" in binary, and its least unused submask is "110" = 6, thus a(8) = 6. %o A303763 (PARI) %o A303763 up_to = (2^14)-1; %o A303763 A006519(n) = (2^valuation(n, 2)); %o A303763 v303763 = vector(up_to); %o A303763 m303764 = Map(); %o A303763 prev=1; for(n=1,up_to,for(m=1,prev,if((bitor(prev,m)==prev) && !mapisdefined(m303764,m),v303763[n] = m;mapput(m303764,m,n);break)); if(!v303763[n], while(mapisdefined(m303764,prev), prev += A006519(1+prev)); v303763[n] = prev; mapput(m303764,prev,n)); prev = v303763[n]); %o A303763 A303763(n) = if(!n,n,v303763[n]); %o A303763 A303764(n) = if(!n,n,mapget(m303764,n)); %Y A303763 Cf. A303764 (inverse). %Y A303763 Cf. A303765, A303767 for similar permutations. %K A303763 nonn,base %O A303763 0,3 %A A303763 _Antti Karttunen_, May 02 2018