A004759 Binary expansion starts 111.

7, 14, 15, 28, 29, 30, 31, 56, 57, 58, 59, 60, 61, 62, 63, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244

Offset

1,1

Comments

This is the minimal recursive sequence such that a(1)=7, A007814(a(n))= A007814(n) and A010060(a(n))=A010060(n). - Vladimir Shevelev, Apr 23 2009

Links

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

Formula

a(2n) = 2a(n), a(2n+1) = 2a(n) + 1 + 6[n==0].

a(n) = n + 6 * 2^floor(log_2(n)) = A004758(n) + A053644(n).

a(n+1) = min{m > a(n): A007814(m) = A007814(n+1) and A010060(m) = A010060(n+1)}. a(2^k) - a(2^k-1) = A103204(k+2), k >= 1. - Vladimir Shevelev, Apr 23 2009

a(2^m+k) = 7*2^m + k, m >= 0, 0 <= k < 2^m. - Yosu Yurramendi, Aug 08 2016

Example

30 in binary is 11110, so 30 is in sequence.

Mathematica

w = {1, 1, 1}; Select[Range[5, 244], If[# < 2^(Length@ w - 1), True, Take[IntegerDigits[#, 2], Length@ w] == w] &] (* Michael De Vlieger, Aug 10 2016 *)
Sort[FromDigits[#, 2]&/@(Flatten[Table[Join[{1, 1, 1}, #]&/@Tuples[{1, 0}, n], {n, 0, 5}], 1])] (* Harvey P. Dale, Sep 01 2016 *)

Prog

(PARI) a(n)=n+6*2^floor(log(n)/log(2))
(Haskell)
import Data.List (transpose)
a004759 n = a004759_list !! (n-1)
a004759_list = 7 : concat (transpose [zs, map (+ 1) zs])
                   where zs = map (* 2) a004759_list
-- Reinhard Zumkeller, Dec 03 2015
(Python)
def A004759(n): return n+(3<<n.bit_length()) # Chai Wah Wu, Jul 13 2022

Crossrefs

Cf. A004754 (10), A004755 (11), A004756 (100), A004757 (101), A004758 (110).

Cf. A004760, A053644, A062050, A076877.

Cf. A007814, A010060, A103204, A159559, A159560, A159615, A159619, A159629, A159698. -Vladimir Shevelev, Apr 23 2009

Sequence in context: A069137 A141164 A004781 * A364287 A062056 A173024

Adjacent sequences: A004756 A004757 A004758 * A004760 A004761 A004762

Keyword

nonn,base,easy

Author

N. J. A. Sloane

Extensions

Edited by Ralf Stephan, Oct 12 2003

Status

approved