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A033052 a(1) = 1, a(2n) = 16a(n), a(2n+1) = a(2n)+1. 19
0, 1, 16, 17, 256, 257, 272, 273, 4096, 4097, 4112, 4113, 4352, 4353, 4368, 4369, 65536, 65537, 65552, 65553, 65792, 65793, 65808, 65809, 69632, 69633, 69648, 69649, 69888, 69889, 69904, 69905, 1048576, 1048577, 1048592, 1048593, 1048832 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Numbers whose set of base 16 digits is {0,1}.

a(n) = Xpower(n,4). - Antti Karttunen, Apr 26 1999

Sums of distinct powers of 16.

For every nonnegative n, A000695(n) is a unique sum of the form a(k)+4a(l). Thus every nonnegative n is a unique sum of the form a(p)+2a(q)+4a(r)+8a(s). This gives a one-to-one map of the set N_0 of all nonnegative integers to (N_0)^4. Furthermore, if, for a fixed positive integer m, to consider all sums of distinct powers of 4^m, then one can obtain a one-to-one map of the set N_0 to (N_0)^(2^m). [Vladimir Shevelev, Nov 14 2008]

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = Sum{d(i)*16^i: i=0, 1, ..., m}, where Sum{d(i)*2^i: i=0, 1, ..., m} is the base 2 representation of n.

a(n) = A097262(n)/15.

a(2n) = 16*a(n), a(2n+1) = a(2n)+1.

a(n) = Sum_k>=0 {A030308(n,k)*16^k}. - Philippe Deléham, Oct 19 2011.

G.f.: (1/(1 - x))*Sum_{k>=0} 16^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017

MATHEMATICA

FromDigits[#, 16]&/@Tuples[{0, 1}, 5] (* Vincenzo Librandi, Jun 04 2012 *)

PROG

(MAGMA) [n: n in [1..1050000] | Set(IntegerToSequence(n, 16)) subset {0, 1}]; // Vincenzo Librandi, May 04 2012

(PARI) a(n)=n=Vecrev(binary(n)); sum(i=1, #n, n[i]<<(4*i))>>4 \\ Charles R Greathouse IV, Sep 23 2012

CROSSREFS

Cf. A000695, A005836, A033042-A033051.

Column 4 of A048723. Row 15 of array A104257.

Sequence in context: A041534 A041536 A041538 * A041540 A041541 A041542

Adjacent sequences:  A033049 A033050 A033051 * A033053 A033054 A033055

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling

EXTENSIONS

Extended by Ray Chandler, Aug 03 2004

Simpler definition from Ralf Stephan, Jun 18 2005

STATUS

approved

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Last modified January 20 10:23 EST 2018. Contains 297960 sequences.