A338500 - OEIS

%I #13 Nov 03 2020 03:24:21

%S 0,1,2,4,3,5,6,8,7,9,11,13,16,10,17,12,18,20,14,21,24,19,28,32,15,25,

%T 22,33,23,36,26,37,27,29,34,64,30,48,31,41,65,35,68,38,44,39,52,45,54,

%U 69,40,66,49,51,53,46,80,42,81,43,73,47,84,50,72,55,57,67

%N Lexicographically earliest sequence of distinct nonnegative terms such that for any n >= 0, a(n) AND a(n+1) is a square (where AND denotes the bitwise AND operator).

%C This sequence is a permutation of the nonnegative integers with inverse A334672:

%C - we can always extend the sequence with a power of 4,

%C - eventually every power of 4 appears in the sequence,

%C - a power of 4 is followed by the least value not yet in the sequence,

%C - so eventually every integer will appear.

%H Rémy Sigrist, <a href="/A338500/b338500.txt">Table of n, a(n) for n = 0..10000</a>

%H Rémy Sigrist, <a href="/A338500/a338500.gp.txt">PARI program for A338500</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%e The first terms, alongside a(n) AND a(n+1), are:

%e   n   a(n)  a(n) AND a(n+1)

%e   --  ----  ---------------

%e    0     0              0^2

%e    1     1              0^2

%e    2     2              0^2

%e    3     4              0^2

%e    4     3              1^2

%e    5     5              2^2

%e    6     6              0^2

%e    7     8              0^2

%e    8     7              1^2

%e    9     9              3^2

%e   10    11              3^2

%e   11    13              0^2

%e   12    16              0^2

%o (PARI) See Links section.

%Y Cf. A334672 (inverse), A335615, A338501.

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, Oct 31 2020