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A004754 Numbers n whose binary expansion starts 10. 24
2, 4, 5, 8, 9, 10, 11, 16, 17, 18, 19, 20, 21, 22, 23, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 128, 129, 130, 131 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A000120(a(n)) = A000120(n); A023416(a(n-1)) = A008687(n) for n > 1. - Reinhard Zumkeller, Dec 04 2015

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

Index entries for sequences related to binary expansion of n

FORMULA

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

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

a(2^m+k) = 2^(m+1) + k, m >= 0, 0 <= k < 2^m. - Yosu Yurramendi, Aug 08 2016

EXAMPLE

10 in binary is 1010, so 10 is in sequence.

MATHEMATICA

w = {1, 0}; Select[Range[2, 131], If[# < 2^(Length@ w - 1), True, Take[IntegerDigits[#, 2], Length@ w] == w] &] (* Michael De Vlieger, Aug 08 2016 *)

PROG

(PARI) a(n)=n+2^floor(log(n)/log(2))

(PARI) is(n)=n>1 && !binary(n)[2] \\ Charles R Greathouse IV, Sep 23 2012

(Haskell)

import Data.List (transpose)

a004754 n = a004754_list !! (n-1)

a004754_list = 2 : concat (transpose [zs, map (+ 1) zs])

                   where zs = map (* 2) a004754_list

-- Reinhard Zumkeller, Dec 04 2015

CROSSREFS

Cf. A123001 (binary version), A004755 (11), A004756 (100), A004757 (101), A004758 (110), A004759 (111).

Cf. A004760, A053644, A062050, A076877.

Apart from initial terms, same as A004761.

Cf. A000120, A023416, A008687.

Sequence in context: A175141 A072756 A004761 * A322014 A010450 A035231

Adjacent sequences:  A004751 A004752 A004753 * A004755 A004756 A004757

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Edited by Ralf Stephan, Oct 12 2003

STATUS

approved

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Last modified January 19 21:52 EST 2019. Contains 319310 sequences. (Running on oeis4.)