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

1,1

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

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

Example

18 in binary is 10010, so 18 is in sequence.

Mathematica

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

Prog

(PARI) a(n)=n+3*2^floor(log(n)/log(2))
(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
(Python)
def A004756(n): return n+(3<<n.bit_length()-1) # Chai Wah Wu, Jul 13 2022

Crossrefs

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

Cf. A004760, A053644, A062050, A076877.

Sequence in context: A141066 A018196 A072103 * A237882 A153034 A106840

Adjacent sequences: A004753 A004754 A004755 * A004757 A004758 A004759

Keyword

nonn,easy,base

Author

N. J. A. Sloane

Extensions

Edited by Ralf Stephan, Oct 12 2003

Status

approved