A004757 Binary expansion starts 101.

5, 10, 11, 20, 21, 22, 23, 40, 41, 42, 43, 44, 45, 46, 47, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Examples

			22 in binary is 10110, so 22 is in sequence.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..4095

Crossrefs

Cf. A004754 (10), A004755 (11), A004756 (100), A004758 (110), A004759 (111).

Cf. A004760, A053644, A062050, A076877.

Programs

Haskell

import Data.List (transpose)
a004757 n = a004757_list !! (n-1)
a004757_list = 5 : concat (transpose [zs, map (+ 1) zs])
                   where zs = map (* 2) a004757_list
-- Reinhard Zumkeller, Dec 04 2015

Mathematica

Table[n + 4*2^Floor@ Log2@ n, {n, 57}] (* or *)
w = {1, 0, 1}; Select[Range[5, 185], If[# < 2^(Length@ w - 1), True, Take[IntegerDigits[#, 2], Length@ w] == w] &] (* Michael De Vlieger, Aug 10 2016 *)
Select[Range[5,200],Take[IntegerDigits[#,2],3]=={1,0,1}&] (* Harvey P. Dale, Aug 26 2016 *)

PARI

a(n)=n+4*2^floor(log(n)/log(2))

Python

def A004757(n): return n+(2<Chai Wah Wu, Jul 13 2022

Formula

a(2n) = 2a(n), a(2n+1) = 2a(n) + 1 + 4*[n==0].

a(n) = n + 4 * 2^floor(log_2(n)) = A004756(n) + A053644(n).

a(2^m+k) = 5*2^m + k, m >= 0, 0 <= k < 2^m. - Yosu Yurramendi, Aug 08 2016

Extensions

Edited by Ralf Stephan, Oct 12 2003