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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: A306572 A041536 A041538 * A041540 A041541 A041542 Adjacent sequences:  A033049 A033050 A033051 * A033053 A033054 A033055 KEYWORD nonn,base,easy AUTHOR EXTENSIONS Extended by Ray Chandler, Aug 03 2004 Simpler definition from Ralf Stephan, Jun 18 2005 STATUS approved

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Last modified October 23 11:48 EDT 2019. Contains 328345 sequences. (Running on oeis4.)