A175048 Write n in binary, then increase each run of 1's by one 1. a(n) is the decimal equivalent of the result.

3, 6, 7, 12, 27, 14, 15, 24, 51, 54, 55, 28, 59, 30, 31, 48, 99, 102, 103, 108, 219, 110, 111, 56, 115, 118, 119, 60, 123, 62, 63, 96, 195, 198, 199, 204, 411, 206, 207, 216, 435, 438, 439, 220, 443, 222, 223, 112, 227, 230, 231, 236, 475, 238, 239, 120, 243, 246

Offset: 1

Author

Leroy Quet, Dec 02 2009

Keywords

• base
• nonn

Examples

			12 in binary is 1100. Increase each run of 1 by one digit to get 11100, which is 28 in decimal. So a(12) = 28.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A175046, A175047, A348710.

Cf. A030308, A007088.

Programs

Haskell

import Data.List (group)
a175048 = foldr (\b v -> 2 * v + b) 0 . concatMap
   (\bs@(b:_) -> if b == 1 then 1 : bs else bs) . group . a030308_row
-- Reinhard Zumkeller, Jul 05 2013

Mathematica

Table[FromDigits[Flatten[If[MemberQ[#,1],Join[{1},#],#]&/@ Split[ IntegerDigits[ n,2]]],2],{n,60}] (* Harvey P. Dale, Oct 10 2013 *)

Python

def a(n): return int(("0"+bin(n)[2:]).replace("01", "011"), 2)
print([a(n) for n in range(1, 61)]) # Michael S. Branicky, Jul 27 2022

Formula

a(2^n) = 3*2^n. a(4n) = 2*a(2n), a(4n+1) = 4*a(2n)+3, a(4n+2) = 2*a(2n+1), a(4n+3) = 2*a(2n+1)+1. - Chai Wah Wu, Nov 21 2018

Extensions

Extended by Ray Chandler, Dec 18 2009