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A004759
Binary expansion starts 111.
8
7, 14, 15, 28, 29, 30, 31, 56, 57, 58, 59, 60, 61, 62, 63, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244
OFFSET
1,1
COMMENTS
This is the minimal recursive sequence such that a(1)=7, A007814(a(n))= A007814(n) and A010060(a(n))=A010060(n). - Vladimir Shevelev, Apr 23 2009
LINKS
FORMULA
a(2n) = 2a(n), a(2n+1) = 2a(n) + 1 + 6[n==0].
a(n) = n + 6 * 2^floor(log_2(n)) = A004758(n) + A053644(n).
a(n+1) = min{m > a(n): A007814(m) = A007814(n+1) and A010060(m) = A010060(n+1)}. a(2^k) - a(2^k-1) = A103204(k+2), k >= 1. - Vladimir Shevelev, Apr 23 2009
a(2^m+k) = 7*2^m + k, m >= 0, 0 <= k < 2^m. - Yosu Yurramendi, Aug 08 2016
EXAMPLE
30 in binary is 11110, so 30 is in sequence.
MATHEMATICA
w = {1, 1, 1}; Select[Range[5, 244], If[# < 2^(Length@ w - 1), True, Take[IntegerDigits[#, 2], Length@ w] == w] &] (* Michael De Vlieger, Aug 10 2016 *)
Sort[FromDigits[#, 2]&/@(Flatten[Table[Join[{1, 1, 1}, #]&/@Tuples[{1, 0}, n], {n, 0, 5}], 1])] (* Harvey P. Dale, Sep 01 2016 *)
PROG
(PARI) a(n)=n+6*2^floor(log(n)/log(2))
(Haskell)
import Data.List (transpose)
a004759 n = a004759_list !! (n-1)
a004759_list = 7 : concat (transpose [zs, map (+ 1) zs])
where zs = map (* 2) a004759_list
-- Reinhard Zumkeller, Dec 03 2015
(Python)
def A004759(n): return n+(3<<n.bit_length()) # Chai Wah Wu, Jul 13 2022
CROSSREFS
KEYWORD
nonn,base,easy
EXTENSIONS
Edited by Ralf Stephan, Oct 12 2003
STATUS
approved