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 A004754 Numbers n whose binary expansion starts 10. 26
 2, 4, 5, 8, 9, 10, 11, 16, 17, 18, 19, 20, 21, 22, 23, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 128, 129, 130, 131 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A000120(a(n)) = A000120(n); A023416(a(n-1)) = A008687(n) for n > 1. - Reinhard Zumkeller, Dec 04 2015 LINKS T. D. Noe, Table of n, a(n) for n = 1..1023 R. Stephan, Some divide-and-conquer sequences ... R. Stephan, Table of generating functions FORMULA a(2n) = 2a(n), a(2n+1) = 2a(n) + 1 + [n==0]. a(n) = n + 2^floor(log_2(n)) = n + A053644(n). a(2^m+k) = 2^(m+1) + k, m >= 0, 0 <= k < 2^m. - Yosu Yurramendi, Aug 08 2016 EXAMPLE 10 in binary is 1010, so 10 is in sequence. MATHEMATICA 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 *) PROG (PARI) a(n)=n+2^floor(log(n)/log(2)) (PARI) is(n)=n>1 && !binary(n)[2] \\ Charles R Greathouse IV, Sep 23 2012 (Haskell) import Data.List (transpose) a004754 n = a004754_list !! (n-1) a004754_list = 2 : concat (transpose [zs, map (+ 1) zs])                    where zs = map (* 2) a004754_list -- Reinhard Zumkeller, Dec 04 2015 CROSSREFS Cf. A123001 (binary version), A004755 (11), A004756 (100), A004757 (101), A004758 (110), A004759 (111). Cf. A004760, A053644, A062050, A076877. Apart from initial terms, same as A004761. Cf. A000120, A023416, A008687. Sequence in context: A072756 A325429 A004761 * A322014 A010450 A035231 Adjacent sequences:  A004751 A004752 A004753 * A004755 A004756 A004757 KEYWORD nonn,easy AUTHOR EXTENSIONS Edited by Ralf Stephan, Oct 12 2003 STATUS approved

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Last modified April 21 14:40 EDT 2021. Contains 343154 sequences. (Running on oeis4.)