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

1,1

Links

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

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

Example

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.

Mathematica

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

Prog

(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
(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

Crossrefs

Cf. A175046, A175047, A348710.

Cf. A030308, A007088.

Sequence in context: A250177 A333002 A333000 * A294231 A280873 A293437

Adjacent sequences: A175045 A175046 A175047 * A175049 A175050 A175051

Keyword

base,nonn

Author

Leroy Quet, Dec 02 2009

Extensions

Extended by Ray Chandler, Dec 18 2009

Status

approved