|
|
A337238
|
|
Number k such that k and k+1 are both digitally balanced numbers in base 2 (A031443).
|
|
5
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
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.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
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.
|
|
MATHEMATICA
|
digBalQ[n_] := Module[{d = IntegerDigits[n, 2], m}, EvenQ@(m = Length@d) && Count[d, 1] == m/2]; Select[Range[2000], digBalQ[#] && digBalQ[# + 1] &]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|