cp's OEIS Frontend

A337238 Number k such that k and k+1 are both digitally balanced numbers in base 2 (A031443).

%I A337238 #29 Nov 23 2020 02:05:40
%S A337238 9,37,41,49,141,149,153,165,169,177,197,201,209,225,541,557,565,569,
%T A337238 589,597,601,613,617,625,653,661,665,677,681,689,709,713,721,737,781,
%U A337238 789,793,805,809,817,837,841,849,865,901,905,913,929,961,2109,2141,2157,2165
%N A337238 Number k such that k and k+1 are both digitally balanced numbers in base 2 (A031443).
%C A337238 All the terms are of the form 4*k + 1, where k is a digitally balanced number in base 2. Therefore, there are no 3 consecutive numbers that are digitally balanced in base 2.
%C A337238 The number of terms below 2^k is A079309(floor(k/2)-1) for k > 3.
%H A337238 Amiram Eldar, <a href="/A337238/b337238.txt">Table of n, a(n) for n = 1..10000</a>
%F A337238 a(n) = 4*A031443(n) + 1.
%e A337238 9 is a term since the binary representation of 9 is 1001, which contains 2 0's and 2 1's, and the binary representation of 9 + 1 = 10 is 1010, which also contains 2 0's and 2 1's.
%t A337238 digBalQ[n_] := Module[{d = IntegerDigits[n, 2], m}, EvenQ@(m = Length@d) && Count[d, 1] == m/2]; Select[Range[2000], digBalQ[#] && digBalQ[# + 1] &]
%Y A337238 Cf. A031443, A079309, A191292.
%Y A337238 A206374 \ {2} is a subsequence.
%K A337238 nonn,base,easy
%O A337238 1,1
%A A337238 _Amiram Eldar_, Nov 21 2020