OFFSET
1,1
COMMENTS
a(n) is the smallest value > a(n-1) (or > 1 for n=1) for which A001511(a(n)) = A001511(n). - Franklin T. Adams-Watters, Oct 23 2006
LINKS
Kenny Lau, Table of n, a(n) for n = 1..16383 (first 1023 terms from T. D. Noe)
Ralf Stephan, Some divide-and-conquer sequences ...
Ralf Stephan, Table of generating functions
FORMULA
a(2n) = 2*a(n), a(2n+1) = 2*a(n) + 1 + 2*[n==0].
a(n) = 2n + A080079(n). - Benoit Cloitre, Feb 22 2003
G.f.: (1/(1+x)) * (1 + Sum_{k>=0, t=x^2^k} 2^k*(2t+t^2)/(1+t)).
a(n) = n + 2^(floor(log_2(n)) + 1) = n + A062383(n). - Franklin T. Adams-Watters, Oct 23 2006
a(2^m+k) = 2^(m+1) + 2^m + k, m >= 0, 0 <= k < 2^m. - Yosu Yurramendi, Aug 08 2016
EXAMPLE
12 in binary is 1100, so 12 is in the sequence.
MAPLE
a:= proc(n) n+2*2^floor(log(n)/log(2)) end: seq(a(n), n=1..60); # Muniru A Asiru, Oct 16 2018
MATHEMATICA
Flatten[Table[FromDigits[#, 2]&/@(Join[{1, 1}, #]&/@Tuples[{0, 1}, n]), {n, 0, 5}]] (* Harvey P. Dale, Feb 05 2015 *)
PROG
(PARI) a(n)=n+2*2^floor(log(n)/log(2))
(PARI) is(n)=n>2 && binary(n)[2] \\ Charles R Greathouse IV, Sep 23 2012
(Haskell)
import Data.List (transpose)
a004755 n = a004755_list !! (n-1)
a004755_list = 3 : concat (transpose [zs, map (+ 1) zs])
where zs = map (* 2) a004755_list
-- Reinhard Zumkeller, Dec 04 2015
(Python)
f = open('b004755.txt', 'w')
lo = 3
hi = 4
i = 1
while i<16384:
for x in range(lo, hi):
f.write(str(i)+" "+str(x)+"\n")
i += 1
lo <<= 1
hi <<= 1
# Kenny Lau, Jul 05 2016
(Python)
def A004755(n): return n+(1<<n.bit_length()) # Chai Wah Wu, Jul 13 2022
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
EXTENSIONS
Edited by Ralf Stephan, Oct 12 2003
STATUS
approved