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%I #35 Jul 13 2022 20:37:29
%S 2,4,5,8,9,10,11,16,17,18,19,20,21,22,23,32,33,34,35,36,37,38,39,40,
%T 41,42,43,44,45,46,47,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,
%U 80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,128,129,130,131
%N Numbers n whose binary expansion starts 10.
%C A000120(a(n)) = A000120(n); A023416(a(n-1)) = A008687(n) for n > 1. - _Reinhard Zumkeller_, Dec 04 2015
%H T. D. Noe, <a href="/A004754/b004754.txt">Table of n, a(n) for n = 1..1023</a>
%H Ralf Stephan, <a href="/somedcgf.html">Some divide-and-conquer sequences ...</a>
%H Ralf Stephan, <a href="/A079944/a079944.ps">Table of generating functions</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F a(2n) = 2a(n), a(2n+1) = 2a(n) + 1 + [n==0].
%F a(n) = n + 2^floor(log_2(n)) = n + A053644(n).
%F a(2^m+k) = 2^(m+1) + k, m >= 0, 0 <= k < 2^m. - _Yosu Yurramendi_, Aug 08 2016
%e 10 in binary is 1010, so 10 is in sequence.
%t w = {1, 0}; Select[Range[2, 131], If[# < 2^(Length@ w - 1), True, Take[IntegerDigits[#, 2], Length@ w] == w] &] (* _Michael De Vlieger_, Aug 08 2016 *)
%o (PARI) a(n)=n+2^floor(log(n)/log(2))
%o (PARI) is(n)=n>1 && !binary(n)[2] \\ _Charles R Greathouse IV_, Sep 23 2012
%o (Haskell)
%o import Data.List (transpose)
%o a004754 n = a004754_list !! (n-1)
%o a004754_list = 2 : concat (transpose [zs, map (+ 1) zs])
%o where zs = map (* 2) a004754_list
%o -- _Reinhard Zumkeller_, Dec 04 2015
%o (Python)
%o def A004754(n): return n+(1<<n.bit_length()-1) # _Chai Wah Wu_, Jul 13 2022
%Y Cf. A123001 (binary version), A004755 (11), A004756 (100), A004757 (101), A004758 (110), A004759 (111).
%Y Cf. A004760, A053644, A062050, A076877.
%Y Apart from initial terms, same as A004761.
%Y Cf. A000120, A023416, A008687.
%K nonn,easy,base
%O 1,1
%A _N. J. A. Sloane_
%E Edited by _Ralf Stephan_, Oct 12 2003
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