cp's OEIS Frontend

A341911 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the number of ones in the binary expansion of n equals the number of runs in the binary expansion of a(n).

%I A341911 #15 Feb 24 2021 16:25:31
%S A341911 0,1,3,2,7,4,6,5,15,8,12,9,14,11,13,10,31,16,24,17,28,19,23,18,30,25,
%T A341911 27,20,29,22,26,21,63,32,48,33,56,35,39,34,60,47,49,36,51,38,40,37,62,
%U A341911 55,57,44,59,46,50,41,61,52,54,43,58,45,53,42,127,64,96
%N A341911 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the number of ones in the binary expansion of n equals the number of runs in the binary expansion of a(n).
%C A341911 This sequence is a permutation of the nonnegative integers with inverse A341910.
%H A341911 Rémy Sigrist, <a href="/A341911/b341911.txt">Table of n, a(n) for n = 0..8191</a>
%H A341911 Rémy Sigrist, <a href="/A341911/a341911.png">Colored scatterplot of the first 2^16 terms</a> (where the color is function of A000120(n))
%H A341911 Rémy Sigrist, <a href="/A341911/a341911.gp.txt">PARI program for A341911</a>
%H A341911 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A341911 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A341911 A000120(n) = A005811(a(n)).
%F A341911 a(n) < 2^k for any n < 2^k.
%e A341911 The first terms, in decimal and in binary, are:
%e A341911   n   a(n)  bin(n)   bin(a(n))
%e A341911   --  ----  -------  ---------
%e A341911    0     0        0          0
%e A341911    1     1        1          1
%e A341911    2     3       10         11
%e A341911    3     2       11         10
%e A341911    4     7      100        111
%e A341911    5     4      101        100
%e A341911    6     6      110        110
%e A341911    7     5      111        101
%e A341911    8    15     1000       1111
%e A341911    9     8     1001       1000
%e A341911   10    12     1010       1100
%t A341911 Block[{a = {0}, k}, Do[k = 1; While[Nand[FreeQ[a, k], Length[Split@ IntegerDigits[k, 2]] == #], k++] &@ DigitCount[i, 2, 1]; AppendTo[a, k], {i, 66}]; a] (* _Michael De Vlieger_, Feb 24 2021 *)
%o A341911 (PARI) See Links section.
%Y A341911 Cf. A000120, A005811, A298847, A341910 (inverse).
%K A341911 nonn,look,base
%O A341911 0,3
%A A341911 _Rémy Sigrist_, Feb 23 2021