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Numbers in whose binary expansion there are no 1-runs of odd length followed by a 0 to their right.
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%I #28 Aug 17 2020 14:48:27

%S 0,1,3,6,7,12,13,15,24,25,27,30,31,48,49,51,54,55,60,61,63,96,97,99,

%T 102,103,108,109,111,120,121,123,126,127,192,193,195,198,199,204,205,

%U 207,216,217,219,222,223,240,241,243,246,247,252,253,255,384,385,387,390,391,396,397,399,408,409,411,414,415,432

%N Numbers in whose binary expansion there are no 1-runs of odd length followed by a 0 to their right.

%C No runs of 1-bits of odd length allowed in the binary expansion of n (A007088), except that when n is an odd number, then the rightmost run may have an odd length. Subsequence A277335 does not allow that exception.

%C A005940(1+a(n)) yields a permutation of A028982, squares and twice squares.

%C Running maximum without repetition of the decimal equivalent of Gray code for n (A003188). - _Frédéric Nouvier_, Aug 14 2020

%H Antti Karttunen, <a href="/A295897/b295897.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = A003714(n-1) XOR ( A003714(n-1) >> 1 ). - _Frédéric Nouvier_, Aug 14 2020

%o (Scheme, with _Antti Karttunen_'s IntSeq-library)

%o (define A295897 (NONZERO-POS 1 0 A295896))

%o (Rust)

%o fn main() {

%o for i in (0..2048)

%o // Filter to get A003714

%o .filter(|n| n & (n << 1) == 0)

%o // Map to produce A295897

%o .map(|n| n ^ (n >> 1))

%o {

%o println!("{}", i);

%o }

%o } // _Frédéric Nouvier_, Aug 14 2020

%o (Python)

%o [x ^ (x>>1) for x in range(0,2048) if (x & (x<<1) == 0)]

%o # _Frédéric Nouvier_, Aug 14 2020

%Y Cf. A005940, A028982, A280873.

%Y Subsequence of A004760.

%Y Cf. A277335 (a subsequence).

%Y Cf. A295896 (characteristic function).

%K nonn,base

%O 1,3

%A _Antti Karttunen_, Dec 01 2017