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A337582 Numbers m such that m AND (m*2^k) is zero or a power of 2 for any k > 0 (where AND denotes the bitwise AND operator).

%I A337582 #38 Oct 03 2020 10:14:01
%S A337582 0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,22,24,25,26,32,33,34,35,
%T A337582 36,37,38,40,41,44,48,49,50,52,64,65,66,67,68,69,70,72,74,76,80,81,82,
%U A337582 83,88,96,97,98,100,101,104,128,129,130,131,132,133,134,136
%N A337582 Numbers m such that m AND (m*2^k) is zero or a power of 2 for any k > 0 (where AND denotes the bitwise AND operator).
%C A337582 For any k > 0, there are A308251(k-1) positive terms with k binary digits.
%C A337582 The ones in the binary representation of any term encodes a finite set of nonnegative integers, say S, such that the differences between any two distinct elements of S are all unique.
%C A337582 For any m >= 0, m belongs to the sequence iff 2*m belongs to the sequence.
%H A337582 Rémy Sigrist, <a href="/A337582/b337582.txt">Table of n, a(n) for n = 1..10000</a>
%H A337582 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%e A337582 Regarding 7:
%e A337582 - 7 AND 14 = 6, which is neither 0 nor a power of 2,
%e A337582 - so 7 does not belong to the sequence.
%e A337582 Regarding 13:
%e A337582 - we have the following values:
%e A337582     k    13 AND (13*2^k)
%e A337582     ---  ---------------
%e A337582       1              2^3
%e A337582       2              2^2
%e A337582       3              2^3
%e A337582     >=4                0
%e A337582 - so 13 belongs to the sequence.
%o A337582 (PARI) is(n) = { my (m=n); while (m>>=1, if (hammingweight(bitand(m,n))>1, return (0))); return (1) }
%Y A337582 Cf. A308251.
%K A337582 nonn,base
%O A337582 1,3
%A A337582 _Rémy Sigrist_, Sep 20 2020