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A209229 Characteristic function of powers of 2, cf. A000079. 50
0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0

COMMENTS

Essentially the same as A036987 (the Fredholm-Rueppel sequence).

Completely multiplicative with a(2^e)=1, a(p^e)=0 for odd primes p. - Mitch Harris, Apr 19 2005

Moebius transform of A001511. - R. J. Mathar, Jun 20 2014

REFERENCES

Michel Rigo, Formal Languages, Automata and Numeration Systems, 2 vols., Wiley, 2014. Mentions this sequence - see "List of Sequences" in Vol. 2.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for characteristic functions

Index to divisibility sequences

FORMULA

a(A000079(n)) = 1; a(A057716(n)) = 0.

a(n+1) = A036987(n).

a(n) = if n<2 then n else (if n is even then a(n/2) else 0).

The generating function g(x) satisfies g(x) - g(x^2)=x. - Joerg Arndt, May 11 2010

Dirichlet g.f. 1/(1-2^(-s)). - R. J. Mathar, Mar 07 2012

G.f.: x / (1 - x / (1 + x / (1 + x / (1 - x / (1 + x / (1 - x / ...)))))) = x / (1 + b(1) * x / (1 + b(2) * x / (1 + b(3) * x / ...))) where b(n) = (-1)^ A090678(n+1). - Michael Somos, Jan 03 2013

With a(0)=0 removed is convolution inverse of A104977. - Michael Somos, Jan 03 2013

EXAMPLE

x + x^2 + x^4 + x^8 + x^16 + x^32 + x^64 + x^128 + x^256 + x^512 + x^1024 + ...

MATHEMATICA

a[n_] := Boole[n == 2^IntegerExponent[n, 2]]; Table[a[n], {n, 0, 100}] (* Jean-Fran├žois Alcover, May 06 2014 *)

PROG

(Haskell)

a209229 n | n < 2 = n

          | n > 1 = if m > 0 then 0 else a209229 n'

          where (n', m) = divMod n 2

(PARI) a(n)=n==1<<valuation(n, 2) \\ Charles R Greathouse IV, Mar 07 2012

(C) int a (unsigned long n) { return n & !(n & (n-1)); } /* Charles R Greathouse IV, Sep 15 2012 */

(PARI) {a(n) = if( n<2 || n%2, n==1, isprimepower(n) > 0)} /* Michael Somos, Jan 03 2013

CROSSREFS

Cf. A029837 (partial sums), A090678, A104977, A154955 (inverse Dirichlet transform).

Sequence in context: A189011 A189135 A219189 * A284622 A215581 A286493

Adjacent sequences:  A209226 A209227 A209228 * A209230 A209231 A209232

KEYWORD

nonn,mult,easy

AUTHOR

Reinhard Zumkeller, Mar 06 2012

STATUS

approved

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Last modified June 25 20:26 EDT 2017. Contains 288730 sequences.