A004754 Numbers n whose binary expansion starts 10.

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

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

Ralf Stephan, Some divide-and-conquer sequences ...

Ralf Stephan, Table of generating functions

Index entries for sequences related to binary expansion of n

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
(Python)
def A004754(n): return n+(1<<n.bit_length()-1) # Chai Wah Wu, Jul 13 2022

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,base

Author

N. J. A. Sloane

Extensions

Edited by Ralf Stephan, Oct 12 2003

Status

approved