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

9, 37, 41, 49, 141, 149, 153, 165, 169, 177, 197, 201, 209, 225, 541, 557, 565, 569, 589, 597, 601, 613, 617, 625, 653, 661, 665, 677, 681, 689, 709, 713, 721, 737, 781, 789, 793, 805, 809, 817, 837, 841, 849, 865, 901, 905, 913, 929, 961, 2109, 2141, 2157, 2165

Offset: 1

Author

Amiram Eldar, Nov 21 2020

Keywords

• nonn
• base
• easy

Comments

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.

The number of terms below 2^k is A079309(floor(k/2)-1) for k > 3.

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A031443, A079309, A191292.

A206374 \ {2} is a subsequence.

Programs

Mathematica

digBalQ[n_] := Module[{d = IntegerDigits[n, 2], m}, EvenQ@(m = Length@d) && Count[d, 1] == m/2]; Select[Range[2000], digBalQ[#] && digBalQ[# + 1] &]

Formula

a(n) = 4*A031443(n) + 1.