A175047 Write n in binary, then increase each run of 0's by one 0. a(n) is the decimal equivalent of the result.

1, 4, 3, 8, 9, 12, 7, 16, 17, 36, 19, 24, 25, 28, 15, 32, 33, 68, 35, 72, 73, 76, 39, 48, 49, 100, 51, 56, 57, 60, 31, 64, 65, 132, 67, 136, 137, 140, 71, 144, 145, 292, 147, 152, 153, 156, 79, 96, 97, 196, 99, 200, 201, 204, 103, 112, 113, 228, 115, 120, 121, 124, 63, 128

Offset: 1

Author

Leroy Quet, Dec 02 2009

Keywords

• base
• nonn

Comments

From Reinhard Zumkeller, Dec 12 2009: (Start)

A070939(a(n)) = A070939(n) + A033264(n);

A171598 and A171599 give record values and where they occur. (End)

Examples

			12 in binary is 1100. Increase each run of 0 by one digit to get 11000, which is 24 in decimal. So a(12) = 24.
		

Links

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

Crossrefs

Cf. A175046, A175048.

Cf. A084471. - Robert G. Wilson v, Dec 11 2009

Cf. A030308, A106151, A007088.

Programs

Haskell

import Data.List (group)
a175047 = foldr (\b v -> 2 * v + b) 0 . concatMap
   (\bs@(b:_) -> if b == 0 then 0 : bs else bs) . group . a030308_row
-- Reinhard Zumkeller, Jul 05 2013

Mathematica

f[n_] := Block[{s = Split@ IntegerDigits[n, 2]}, FromDigits[ Flatten@ Insert[s, {0}, Table[{2 i}, {i, Floor[ Length@s/2]} ]], 2]]; Array[ f, 64] (* Robert G. Wilson v, Dec 11 2009 *)

Python

from re import split
def A175047(n):
  return int(''.join(d+'0' if '0' in d else d for d in split('(0+)|(1+)',bin(n)[2:]) if d != '' and d != None),2) # Chai Wah Wu, Nov 21 2018

Formula

a(n) = if n<2 then n else 2*(1 + 0^((n+2) mod 4))*a([n/2]) + n mod 2. - Reinhard Zumkeller, Jan 20 2010

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

Extensions

Extended by Ray Chandler, Dec 18 2009

a(11) onwards from Robert G. Wilson v and Reinhard Zumkeller, Dec 11 2009