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A004758
Binary expansion starts 110.
10
6, 12, 13, 24, 25, 26, 27, 48, 49, 50, 51, 52, 53, 54, 55, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213
OFFSET
1,1
LINKS
FORMULA
a(2n) = 2a(n), a(2n+1) = 2a(n) + 1 + 5*[n==0].
a(n) = n + 5 * 2^floor(log_2(n)) = A004757(n) + A053644(n).
a(2^m+k) = 6*2^m + k, m >= 0, 0 <= k < 2^m. - Yosu Yurramendi, Aug 08 2016
EXAMPLE
26 in binary is 11010, so 26 is in sequence.
MATHEMATICA
w = {1, 1, 0}; Select[Range[5, 213], If[# < 2^(Length@ w - 1), True, Take[IntegerDigits[#, 2], Length@ w] == w] &] (* or *)
Table[n + 5*2^Floor@ Log2@ n, {n, 53}] (* Michael De Vlieger, Aug 10 2016 *)
PROG
(PARI) a(n)=n+5*2^floor(log(n)/log(2))
(Haskell)
import Data.List (transpose)
a004758 n = a004758_list !! (n-1)
a004758_list = 6 : concat (transpose [zs, map (+ 1) zs])
where zs = map (* 2) a004758_list
-- Reinhard Zumkeller, Dec 03 2015
(Python)
def A004758(n): return n+(5<<n.bit_length()-1) # Chai Wah Wu, Jul 13 2022
CROSSREFS
Cf. A004754 (10), A004755 (11), A004756 (100), A004757 (101), A004759 (111).
Sequence in context: A297258 A296702 A297135 * A055051 A338054 A336559
KEYWORD
nonn,base,easy
EXTENSIONS
Edited by Ralf Stephan, Oct 12 2003
STATUS
approved