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

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• base

Comments

A000120(a(n)) = A000120(n); A023416(a(n-1)) = A008687(n) for n > 1. - Reinhard Zumkeller, Dec 04 2015

Examples

			10 in binary is 1010, so 10 is in sequence.
		

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

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.

Programs

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

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 *)

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

Python

def A004754(n): return n+(1<Chai Wah Wu, Jul 13 2022

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

Extensions

Edited by Ralf Stephan, Oct 12 2003