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A004756 Binary expansion starts 100. 8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1023

R. Stephan, Some divide-and-conquer sequences ...

R. 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(log2(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

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

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Edited by Ralf Stephan, Oct 12 2003

STATUS

approved

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Last modified October 15 11:03 EDT 2018. Contains 316224 sequences. (Running on oeis4.)