|
| |
| |
|
|
|
0, 1, 2, 4, 6, 8, 10, 13, 16, 19, 22, 25, 28, 31, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 103, 108, 113, 118, 123, 128, 133, 138, 143, 148, 153, 158, 163, 168, 173, 178, 183, 188, 193, 198, 203, 208, 213, 218, 223, 228, 233, 238, 243, 248
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| Given a term b>0 of the sequence and its left hand neighbour c, the corresponding unique sequence index n with property a(n)=b can be determined by n(b)=e+(b-d*(e+1)+2*(e-1))/d, where d=b-c and e=2^d. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Dec 05 2006
|
|
|
REFERENCES
| M. Griffiths, More sums involving the floor function, Math. Gaz., 86 (2002), 285-287.
D. E. Knuth, Fundamental Algorithms, Addison-Wesley, 1973, Section 1.2.4, ex. 42(b).
|
|
|
LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,1000
J.-P. Allouche and J. Shallit, The ring of k-regular sequences, Theoretical Computer Sci., 98 (1992), 163-197, ex. 27.
|
|
|
FORMULA
| a(n) = Sum_{k=1..n} floor(log_2(k)) = (n+1)*floor(log_2(n)) - 2*(2^floor(log_2(n)) - 1). - Diego Torres (torresvillarroel(AT)hotmail.com), Oct 29 2002
G.f.: 1/(1-x)^2 * Sum(k>=1, x^2^k). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 13 2002
|
|
|
MAPLE
| [seq(add(floor(log_2(k)), k=1..j), j=1..100)]
|
|
|
PROG
| (PARI) a(n)=if(n<1, 0, if(n%2==0, a(n/2)+a(n/2-1)+n-1, 2*a((n-1)/2)+n-1)) (from R. Stephan)
(PARI) a(n)=local(k); if(n<1, 0, k=length(binary(n))-1; (n+1)*k-2*(2^k-1))
(PARI) { for (n=1, 1000, k=length(binary(n))-1; write("b061168.txt", n, " ", (n + 1)*k - 2*(2^k - 1)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 18 2009]
|
|
|
CROSSREFS
| Cf. A001855.
a(n) = A001855(n+1)-n.
Sequence in context: A053044 A129011 A130174 * A130798 A165453 A025224
Adjacent sequences: A061165 A061166 A061167 * A061169 A061170 A061171
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Antti Karttunen Apr 19 2001
|
| |
|
|
