A079944 A run of 2^n 0's followed by a run of 2^n 1's, for n=0, 1, 2, ...

0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1

Offset: 0

Author

N. J. A. Sloane, Feb 21 2003

Keywords

• nonn
• easy

Comments

With offset 2, this is the second bit in the binary expansion of n. - Franklin T. Adams-Watters, Feb 13 2009

a(n) = A173920(n+2,2); in the sequence of nonnegative integers (cf. A001477) substitute all n by 2^floor(n/2) occurrences of (n mod 2). - Reinhard Zumkeller, Mar 04 2010

References

• Michel Rigo, Formal Languages, Automata and Numeration Systems, 2 vols., Wiley, 2014. See Example 1.34.

Links

• R. Stephan, Some divide-and-conquer sequences ...
• R. Stephan, Table of generating functions

Crossrefs

Cf. A086694, A079882, A079945, A173922, A173923.

Programs

Haskell

a079944 n = a079944_list !! n
a079944_list =  f [0,1] where f (x:xs) = x : f (xs ++ [x,x])
-- Reinhard Zumkeller, Oct 14 2010, Mar 28 2011

Mathematica

Table[IntegerDigits[n + 2, 2][[2]], {n, 0, 100}] (* Jean-François Alcover, Jul 26 2019 *)

PARI

a(n)=binary(n+2)[2] \\ Charles R Greathouse IV, Nov 07 2016

Formula

a(n) = floor(log[2](4*(n+2)/3)) - floor(log[2](n+2)). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 22 2003

For n >= 2, a(n-2)=1+floor(log[2](n/3))-floor(log[2](n/2)) - Benoit Cloitre, Mar 03 2003

G.f.: 1/x^2/(1-x) * (1/x + sum(k>=0, x^(3*2^k)-x^2^(k+1))). - Ralf Stephan, Jun 04 2003

a(n) = A000035(A004526(A030101(n+2))). - Reinhard Zumkeller, Mar 04 2010