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A079944 A run of 2^n 0's followed by a run of 2^n 1's, for n=0, 1, 2, ... 115
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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

Table of n, a(n) for n=0..98.

R. Stephan, Some divide-and-conquer sequences ...

R. Stephan, Table of generating functions

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

PROG

(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

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

CROSSREFS

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

Sequence in context: A104894 A168393 A071986 * A059652 A108736 A079813

Adjacent sequences:  A079941 A079942 A079943 * A079945 A079946 A079947

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Feb 21 2003

STATUS

approved

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Last modified October 20 12:34 EDT 2018. Contains 316379 sequences. (Running on oeis4.)