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

1,1

Links

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

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

Example

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

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 *)

Prog

(PARI) a(n)=n+4*2^floor(log(n)/log(2))
(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
(Python)
def A004757(n): return n+(2<<n.bit_length()) # Chai Wah Wu, Jul 13 2022

Crossrefs

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

Cf. A004760, A053644, A062050, A076877.

Sequence in context: A136822 A189151 A120513 * A007527 A033894 A033649

Adjacent sequences: A004754 A004755 A004756 * A004758 A004759 A004760

Keyword

nonn,base,easy

Author

N. J. A. Sloane

Extensions

Edited by Ralf Stephan, Oct 12 2003

Status

approved