A004756 Binary expansion starts 100.

4, 8, 9, 16, 17, 18, 19, 32, 33, 34, 35, 36, 37, 38, 39, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• base

Examples

			18 in binary is 10010, so 18 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

Crossrefs

Cf. A004754 (10), A004755 (11), A004757 (101), A004758 (110), A004759 (111).

Cf. A004760, A053644, A062050, A076877.

Programs

Haskell

import Data.List (transpose)
a004756 n = a004756_list !! (n-1)
a004756_list = 4 : concat (transpose [zs, map (+ 1) zs])
                   where zs = map (* 2) a004756_list
-- Reinhard Zumkeller, Dec 04 2015

Mathematica

Select[Range[4, 153], Take[IntegerDigits[#, 2], 3] == {1, 0, 0} &] (* Michael De Vlieger, Aug 07 2016 *)

PARI

a(n)=n+3*2^floor(log(n)/log(2))

Python

def A004756(n): return n+(3<Chai Wah Wu, Jul 13 2022

Formula

a(2n) = 2a(n), a(2n+1) = 2a(n) + 1 + 3*[n==0].

a(n) = n + 3 * 2^floor(log_2(n)) = A004755(n) + A053644(n).

a(2^m+k) = 2^(m+2) + k, m >= 0, 0 <= k < 2^m. - Yosu Yurramendi, Aug 07 2016

Extensions

Edited by Ralf Stephan, Oct 12 2003