

A053645


Distance to largest power of 2 less than or equal to n; write n in binary and change the first digit to zero.


43



0, 0, 1, 0, 1, 2, 3, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
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OFFSET

1,6


COMMENTS

Cf. A083741.
a(A004760(n+1)) = n.  Reinhard Zumkeller, May 20 2009
Triangle read by rows in which row n lists the first 2^n nonnegative integers (A001477), n >= 0. Right border gives A000225. Row sums give A006516. See example.  Omar E. Pol, Oct 17 2013


REFERENCES

J.P. Allouche and J. Shallit, The ring of kregular sequences, Theoretical Computer Sci., 98 (1992), 163197 (see Ex. 24).


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
J.P. Allouche and J. Shallit, The ring of kregular sequences, Theoretical Computer Sci., 98 (1992), 163197.
Index entries for sequences related to binary expansion of n


FORMULA

a(n) = n2^A000523(n).
G.f.: 1/(1x) * ((2x1)/(1x) + sum_{k>=1} 2^(k1)*x^2^k).  Ralf Stephan, Apr 18 2003
a(n) = (A006257(n)1)/2.  N. J. A. Sloane, May 16 2003
a(1) = 0, a(2n) = 2a(n), a(2n+1) = 2a(n)+1.  N. J. A. Sloane, Sep 13 2003
a(n) = A062050(n)  1.  N. J. A. Sloane, Jun 12 2004
a(n) = f(n1,1) with f(n,m) = if n<m then n else f(nm,2*m).  Reinhard Zumkeller, May 20 2009


EXAMPLE

From Omar E. Pol, Oct 17 2013: (Start)
Written as an irregular triangle the sequence begins:
0;
0,1;
0,1,2,3;
0,1,2,3,4,5,6,7;
0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15;
0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31;
(End)


MAPLE

seq(n  2^ilog2(n), n=1..1000); # Robert Israel, Dec 23 2015


PROG

(Haskell)
a053645 1 = 0
a053645 n = 2 * a053645 n' + b where (n', b) = divMod n 2
 Reinhard Zumkeller, Aug 28 2014
a053645_list = concatMap (0 `enumFromTo`) a000225_list
 Reinhard Zumkeller, Feb 04 2013, Mar 23 2012
(PARI) a(n)=n2^(#binary(n)1) \\ Charles R Greathouse IV, Sep 02 2015


CROSSREFS

Cf. A053644, A002262, A160588, A000225, A030308.
Sequence in context: A049263 A014588 A278164 * A212598 A274650 A170899
Adjacent sequences: A053642 A053643 A053644 * A053646 A053647 A053648


KEYWORD

nonn,easy


AUTHOR

Henry Bottomley, Mar 22 2000


STATUS

approved



