%I #27 Jul 14 2022 02:36:55
%S 6,12,13,24,25,26,27,48,49,50,51,52,53,54,55,96,97,98,99,100,101,102,
%T 103,104,105,106,107,108,109,110,111,192,193,194,195,196,197,198,199,
%U 200,201,202,203,204,205,206,207,208,209,210,211,212,213
%N Binary expansion starts 110.
%H Reinhard Zumkeller, <a href="/A004758/b004758.txt">Table of n, a(n) for n = 1..4095</a>
%F a(2n) = 2a(n), a(2n+1) = 2a(n) + 1 + 5*[n==0].
%F a(n) = n + 5 * 2^floor(log_2(n)) = A004757(n) + A053644(n).
%F a(2^m+k) = 6*2^m + k, m >= 0, 0 <= k < 2^m. - _Yosu Yurramendi_, Aug 08 2016
%e 26 in binary is 11010, so 26 is in sequence.
%t w = {1, 1, 0}; Select[Range[5, 213], If[# < 2^(Length@ w - 1), True, Take[IntegerDigits[#, 2], Length@ w] == w] &] (* or *)
%t Table[n + 5*2^Floor@ Log2@ n, {n, 53}] (* _Michael De Vlieger_, Aug 10 2016 *)
%o (PARI) a(n)=n+5*2^floor(log(n)/log(2))
%o (Haskell)
%o import Data.List (transpose)
%o a004758 n = a004758_list !! (n-1)
%o a004758_list = 6 : concat (transpose [zs, map (+ 1) zs])
%o where zs = map (* 2) a004758_list
%o -- _Reinhard Zumkeller_, Dec 03 2015
%o (Python)
%o def A004758(n): return n+(5<<n.bit_length()-1) # _Chai Wah Wu_, Jul 13 2022
%Y Cf. A004754 (10), A004755 (11), A004756 (100), A004757 (101), A004759 (111).
%Y Cf. A004760, A053644, A062050, A076877.
%K nonn,base,easy
%O 1,1
%A _N. J. A. Sloane_
%E Edited by _Ralf Stephan_, Oct 12 2003
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