cp's OEIS Frontend

A380358 Numbers whose binary expansion ends with 11 and does not contain adjacent zeros.

%I A380358 #26 Feb 12 2025 18:44:37
%S A380358 3,7,11,15,23,27,31,43,47,55,59,63,87,91,95,107,111,119,123,127,171,
%T A380358 175,183,187,191,215,219,223,235,239,247,251,255,343,347,351,363,367,
%U A380358 375,379,383,427,431,439,443,447,471,475,479,491,495,503,507,511,683
%N A380358 Numbers whose binary expansion ends with 11 and does not contain adjacent zeros.
%C A380358 The numbers in this sequence appear in the conversion of conventional binary numbers to the canonical signed-digit representation.
%D A380358 J. L. Smith and A. Weinberger, "Shortcut Multiplication for Binary Digital Computers", in Methods for High-Speed Addition and Multiplication, National Bureau of Standards Circular 591, Sec. 1, February, 1958, page 21.
%H A380358 R. J. Cintra, <a href="https://arxiv.org/abs/2501.10908">A note on the conversion of nonnegative integers to the canonical signed-digit representation</a>, arXiv:2501.10908 [eess.SP], 2025.
%F A380358 a(n) = 2 * A247648(n) + 1.
%F A380358 From _Hugo Pfoertner_, Feb 07 2025: (Start)
%F A380358 a(n) = 4*A052499(n) - 1.
%F A380358 a(n) = 4*(A365808(n+1) + 1)/3 - 1.
%F A380358 a(n) = 2*(A365809(n) + 1)/3 - 1. (End)
%e A380358 183 is in the sequence because its binary expansion is 10110111.
%t A380358 Select[4*Range[0, 170] + 3, SequencePosition[IntegerDigits[#, 2], {0, 0}] == {} &] (* _Amiram Eldar_, Feb 05 2025 *)
%o A380358 (Python)
%o A380358 from itertools import count, islice
%o A380358 def A380358_gen(startvalue=1): # generator of terms >= startvalue
%o A380358     return filter(lambda n:n&3==3 and not '00' in bin(n),count(max(startvalue,1)))
%o A380358 A380358_list = list(islice(A380358_gen(),20)) # _Chai Wah Wu_, Feb 12 2025
%Y A380358 Cf. A003754, A052499, A247648, A365808, A365809.
%K A380358 nonn,base
%O A380358 1,1
%A A380358 _R. J. Cintra_, Jan 22 2025