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a(0) = 0; a(1) = 1; for n > 1, a(n) = 1 + 4*A092246(n-1).
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%I #19 Mar 04 2023 00:13:13

%S 0,1,5,29,45,53,77,85,101,125,141,149,165,189,197,221,237,245,269,277,

%T 293,317,325,349,365,373,389,413,429,437,461,469,485,509,525,533,549,

%U 573,581,605,621,629,645,669,685,693,717,725,741,765,773,797,813,821,845,853,869,893,909,917,933,957,965,989,1005

%N a(0) = 0; a(1) = 1; for n > 1, a(n) = 1 + 4*A092246(n-1).

%C Seems to be also the fixed points of permutations A268823 and A268824.

%H Antti Karttunen, <a href="/A268673/b268673.txt">Table of n, a(n) for n = 0..10000</a>

%F a(0) = 0; a(1) = 1; for n > 1, a(n) = 1 + 4*A092246(n-1).

%t Join[{0, 1}, 1 + 4 Select[Range[1, 251, 2], OddQ[Total[IntegerDigits[#, 2]]]&]] (* _Jean-François Alcover_, Mar 15 2016 *)

%o (Scheme)

%o (define (A268673 n) (if (<= n 1) n (+ 1 (* 4 (A092246 (- n 1))))))

%o (Python)

%o def A268673(n): return (((m:=n-2)<<4)+(13 if m.bit_count()&1 else 5)) if n>1 else n # _Chai Wah Wu_, Mar 03 2023

%Y Cf. A268823, A268824.

%Y Cf. also A092246, A268717.

%Y Many (but not all) terms of A013710 seem to be included.

%K nonn

%O 0,3

%A _Antti Karttunen_, Feb 19 2016