|
Search: id:A089398
|
|
|
| A089398 |
|
a(n) = n-th column sum of binary digits of k*2^(k-1), where summation is over all k>=1, without carrying from columns sums that may exceed 2. |
|
+0
7
|
|
| 1, 0, 2, 1, 1, 1, 3, 2, 2, 0, 3, 2, 2, 2, 4, 3, 3, 1, 2, 2, 2, 2, 4, 3, 3, 1, 4, 3, 3, 3, 5, 4, 4, 2, 3, 1, 2, 2, 4, 3, 3, 1, 4, 3, 3, 3, 5, 4, 4, 2, 3, 3, 3, 3, 5, 4, 4, 2, 5, 4, 4, 4, 6, 5, 5, 3, 4, 2, 1, 2, 4, 3, 3, 1, 4, 3, 3, 3, 5, 4, 4, 2, 3, 3, 3, 3, 5, 4, 4, 2, 5, 4, 4, 4, 6, 5, 5, 3, 4, 2, 3, 3, 5, 4, 4
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
sum(k=1,n, a(k)*2^(k-1)) = 2^A089399(n)+1 for n>2, with a(1)=a(2)=1.
Row sums of triangular arrays in A103588 and in A103589. - Philippe DELEHAM, Apr 04 2005
a(k) = 0 for k = 2, 10, 2058, 2058 + 2^2059, ..., that is, for k = A034797(n) - 1, n>=2. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 16 2007
|
|
FORMULA
|
a(2^n)=n-1 (for n>0), a(2^n-1)=n (for n>0), a(2^n+1)=n-1 (for n>1), a(2^n-k)=n-A089400(k) (for n>k>0), a(2^n+k)=n-A089401(k) (for n>k>0), where sequences have limits: A089400={0, 2, 2, 2, 1, 4, 2, 2, 1, 3, 3, ...} and A089401={1, 1, 3, 2, 4, 5, 6, 5, 7, 8, 11, 9, ...},
|
|
EXAMPLE
|
Binary expansions of k*2^(k-1), with bits in ascending order by powers of 2, are:
1
001
0011
000001
0000101
00000011
000000111
00000000001
000000001001
0000000000101
00000000001101
000000000000011
0000000000001011
.................
Giving column sums:
10211132203222433...
|
|
MATHEMATICA
|
f[n_] := Block[{lg = Floor[Log[2, n]] + 1}, Sum[ Join[ Reverse[ IntegerDigits[n - i + 1, 2]], {0}][[i]], {i, lg}]]; Table[ f[n], {n, 105}] (from Robert G. Wilson v Mar 26 2005)
|
|
CROSSREFS
|
Cf. A089399, A089400, A089401.
Sequence in context: A086291 A016442 A076360 this_sequence A047040 A047020 A127832
Adjacent sequences: A089395 A089396 A089397 this_sequence A089399 A089400 A089401
|
|
KEYWORD
|
base,nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Oct 30 2003
|
|
|
Search completed in 0.002 seconds
|
