|
Search: id:A078822
|
|
|
| A078822 |
|
Number of distinct binary numbers contained as substrings in binary representation of n. |
|
+0
15
|
|
| 1, 1, 3, 2, 4, 4, 5, 3, 5, 5, 5, 6, 7, 7, 7, 4, 6, 6, 6, 7, 7, 6, 8, 8, 9, 9, 9, 9, 10, 10, 9, 5, 7, 7, 7, 8, 7, 8, 9, 9, 9, 9, 7, 9, 11, 10, 11, 10, 11, 11, 11, 11, 12, 11, 11, 12, 13, 13, 13, 13, 13, 13, 11, 6, 8, 8, 8, 9, 8, 9, 10, 10, 9, 8, 10, 11, 11, 12, 12, 11, 11, 11, 11, 12, 10, 8
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
For k>0: a(2^k-2)=2*(k-1)+1, a(2^k-1)=k, a(2^k)=k+2;
for k>1: a(2^k+1)=k+2;
for k>0: a(2^k-1)=A078824(2^k-1), a(2^k)=A078824(2^k).
For n>0: 0<a(2*n)-a(n)<=A070939(n)+1, 0<a(2*n+1)-a(n)<A070939(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 07 2008
|
|
LINKS
|
R. Zumkeller, Table of n, a(n) for n = 0..1000
|
|
EXAMPLE
|
n=10 -> '1010' contains 5 different binary numbers: '0' (b0bb or bbb0), '1' (1bbb or bb1b), '10' (10bb or bb10), '101' (101b) and '1010' itself, therefore a(10)=5.
|
|
CROSSREFS
|
Cf. A078823, A078826, A078824, A007088.
Sequence in context: A128220 A134749 A061901 this_sequence A069745 A112199 A059851
Adjacent sequences: A078819 A078820 A078821 this_sequence A078823 A078824 A078825
|
|
KEYWORD
|
nonn,base,nice
|
|
AUTHOR
|
Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Dec 08 2002
|
|
|
Search completed in 0.002 seconds
|
