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A175047
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Write n in binary, then increase each run of 0's by one 0. a(n) is the decimal equivalent of the result.
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10
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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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)
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LINKS
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R. Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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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
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EXAMPLE
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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.
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MATHEMATICA
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f[n_] := Block[{s = Split@ IntegerDigits[n, 2]}, FromDigits[ Flatten@ Insert[s, {0}, Table[{2 i}, {i, Floor[ Length@s/2]} ]], 2]]; Arrar[ f, 64] (* Robert G. Wilson v, Dec 11 2009 *)
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PROG
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(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
(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
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CROSSREFS
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Cf. A175046, A175048.
Cf. A084471. - Robert G. Wilson v, Dec 11 2009
Cf. A030308, A106151, A007088.
Sequence in context: A171527 A240969 A198576 * A316688 A309517 A105185
Adjacent sequences: A175044 A175045 A175046 * A175048 A175049 A175050
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KEYWORD
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base,nonn
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AUTHOR
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Leroy Quet, Dec 02 2009
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EXTENSIONS
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Extended by Ray Chandler, Dec 18 2009
a(11) onwards from Robert G. Wilson v and Reinhard Zumkeller, Dec 11 2009
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STATUS
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approved
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