A004758 Binary expansion starts 110.

6, 12, 13, 24, 25, 26, 27, 48, 49, 50, 51, 52, 53, 54, 55, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Examples

			26 in binary is 11010, so 26 is in sequence.
		

Links

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

Crossrefs

Cf. A004754 (10), A004755 (11), A004756 (100), A004757 (101), A004759 (111).

Cf. A004760, A053644, A062050, A076877.

Programs

Haskell

import Data.List (transpose)
a004758 n = a004758_list !! (n-1)
a004758_list = 6 : concat (transpose [zs, map (+ 1) zs])
                   where zs = map (* 2) a004758_list
-- Reinhard Zumkeller, Dec 03 2015

Mathematica

w = {1, 1, 0}; Select[Range[5, 213], If[# < 2^(Length@ w - 1), True, Take[IntegerDigits[#, 2], Length@ w] == w] &] (* or *)
Table[n + 5*2^Floor@ Log2@ n, {n, 53}] (* Michael De Vlieger, Aug 10 2016 *)

PARI

a(n)=n+5*2^floor(log(n)/log(2))

Python

def A004758(n): return n+(5<Chai Wah Wu, Jul 13 2022

Formula

a(2n) = 2a(n), a(2n+1) = 2a(n) + 1 + 5*[n==0].

a(n) = n + 5 * 2^floor(log_2(n)) = A004757(n) + A053644(n).

a(2^m+k) = 6*2^m + k, m >= 0, 0 <= k < 2^m. - Yosu Yurramendi, Aug 08 2016

Extensions

Edited by Ralf Stephan, Oct 12 2003