A304747 - OEIS

%I #12 May 27 2018 19:44:43

%S 0,1,11,10,110,100,101,111,1111,1000,1001,1011,1010,1110,1100,1101,

%T 11101,10000,10001,10011,10010,10110,10100,10101,10111,11111,11000,

%U 11001,11011,11010,11110,11100,111100,100000,100001,100011,100010,100110,100100,100101,100111,101111,101000,101001,101011,101010,101110,101100,101101

%N May code shown in binary: a(n) = A007088(A303767(n)).

%H Antti Karttunen, <a href="/A304747/b304747.txt">Table of n, a(n) for n = 0..8191</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F a(n) = A007088(A303767(n)).

%e The code can be constructed by the rule: a(n+1) is either the least number obtained from a(n) by toggling one or more 1-bits off if no such number is yet in the sequence, otherwise the least number not yet in sequence that can be obtained from a(n) by toggling one 0-bit on:

%e    n    a(n)

%e    0      0

%e    1      1

%e    2     11

%e    3     10

%e    4    110

%e    5    100

%e    6    101

%e    7    111

%e    8   1111

%e    9   1000

%e   10   1001

%e   11   1011

%e   12   1010

%e   13   1110

%e   14   1100

%e   15   1101

%e   16  11101

%e   17  10000

%e   18  10001

%e   19  10011

%e   20  10010

%e   21  10110

%e   22  10100

%e   23  10101

%e   24  10111

%e   25  11111

%e   26  11000

%e   27  11001

%e   28  11011

%e   29  11010

%e   30  11110

%e   31  11100

%e   32 111100

%e   33 100000

%o (PARI)

%o A209229(n) = (n && !bitand(n,n-1));

%o A053644(n) = { my(k=1); while(k<=n, k<<=1); (k>>1); }; \\ From A053644

%o A303767(n) = if(!n,n,if(A209229(n),n+A303767(n-1),A053644(n)+A303767(n-A053644(n)-1)));

%o A007088(n) = fromdigits(binary(n), 10); \\ From A007088.

%o A304747(n) = A007088(A303767(n));

%Y Cf. A007088, A303767.

%Y Cf. also A304749.

%K nonn,base

%O 0,3

%A _Antti Karttunen_, May 23 2018